diff --git a/Julio/problems.ipynb b/Julio/problems.ipynb new file mode 100644 index 00000000..0f3f520f --- /dev/null +++ b/Julio/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":2,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":3,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":3,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAeoAAAKyCAYAAAAaWJ09AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABI0klEQVR4nO3dcVhVdb7v8c8GYqMJpBkbUZQs0xwTDJRB63RmYuJ6fLxxn3saxuMciaw5FRa2b1PRNFLTXLenmbrWSJpOac/p+mj1jNY0hRGj9vSIx4ThXq20LCcoA/SeZCM10GGv+we5cycgxtqs396+X8+zHlk/fmut7y/MD2ut31rbZVmWJQAAYKQYpwsAAAB9I6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGBxThdgh0AgoCNHjigxMVEul8vpcgAA6JdlWWpvb1daWppiYvo/Z46KoD5y5IjS09OdLgMAgLPS1NSkcePG9dsnKoI6MTFRUs+Ak5KSHK4GAID++f1+paenB/OrP1ER1CcvdyclJRHUAICIMZDbtUwmAwDAYFFxRg0E9fbbKR8QByCChe2MurKyUhkZGUpISFBubq727NnTZ98//OEPysnJ0QUXXKDzzz9fWVlZ+rd/+7dwlYZo1dclJJ4EABDBwhLUmzdvltfrVUVFherr65WZmamCggK1trb22n/UqFH6xS9+odraWv3f//t/VVJSopKSEm3bti0c5SEanSmMCWsAEcplWfZfF8zNzdXMmTO1atUqST3POaenp+uOO+7QfffdN6B9XHnllZo3b54efvjhM/b1+/1KTk5WW1sbk8nORWcTwlwGB2CAs8kt28+ou7q6VFdXp/z8/G8OEhOj/Px81dbWnnF7y7JUU1OjgwcP6u/+7u/sLg8AgIhi+2SyY8eOqbu7Wx6PJ6Td4/HowIEDfW7X1tamsWPHqrOzU7GxsXryySf1ox/9qNe+nZ2d6uzsDK77/X57igcAwDDGzPpOTExUQ0ODTpw4oZqaGnm9Xk2cOFF///d/f1pfn8+nhx56aOiLBABgiNke1KNHj1ZsbKxaWlpC2ltaWpSamtrndjExMbr00kslSVlZWXrvvffk8/l6Dery8nJ5vd7g+sk3vAAAEG1sv0cdHx+v7Oxs1dTUBNsCgYBqamqUl5c34P0EAoGQy9uncrvdwbeQ8TYyDHiCGBPJAESgsFz69nq9Ki4uVk5OjmbNmqWVK1eqo6NDJSUlkqRFixZp7Nix8vl8knouZefk5OiSSy5RZ2enXn31Vf3bv/2bVq9eHY7yEI0sq//Z34Q0gAgVlqAuKirS0aNHtWzZMjU3NysrK0tVVVXBCWaNjY0hH+vV0dGh22+/XZ988omGDRumKVOm6LnnnlNRUVE4ykO06iusCWkAESwsz1EPNZ6jRtC3gzry/3oDiEKOPkcNAADsQ1ADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADCYMR/KgSHCC0EAIKJwRn0u6esVm/29ehMA4CiC+lxxpjAmrAHASAT1uWCgIUxYA4BxCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKA+Fwz0OWmepwYA4xDU54ozhTAhDQBGIqjPJX2FMSENAMYiqM91hDQAGI2gBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGi3O6AAAD5HKd3mZZQ18HgCEVtjPqyspKZWRkKCEhQbm5udqzZ0+ffdetW6err75aI0eO1MiRI5Wfn99vf+Cc01tI99cOIGqEJag3b94sr9eriooK1dfXKzMzUwUFBWptbe21/44dO7RgwQJt375dtbW1Sk9P13XXXadPP/00HOUBkeVMYUxYA1HNZVn2XzvLzc3VzJkztWrVKklSIBBQenq67rjjDt13331n3L67u1sjR47UqlWrtGjRojP29/v9Sk5OVltbm5KSkgZdf1T79j/q0XbpNNrGdzYhHOljBc4hZ5Nbtp9Rd3V1qa6uTvn5+d8cJCZG+fn5qq2tHdA+vvjiC3311VcaNWqU3eUBABBRbJ9MduzYMXV3d8vj8YS0ezweHThwYED7uPfee5WWlhYS9qfq7OxUZ2dncN3v93/3ggEAMJhxj2etWLFCmzZt0pYtW5SQkNBrH5/Pp+Tk5OCSnp4+xFUCADA0bA/q0aNHKzY2Vi0tLSHtLS0tSk1N7Xfb3/72t1qxYoVef/11TZ8+vc9+5eXlamtrCy5NTU221A4AgGlsD+r4+HhlZ2erpqYm2BYIBFRTU6O8vLw+t3vkkUf08MMPq6qqSjk5Of0ew+12KykpKWQBotJAJ4gxkQyIWmF54YnX61VxcbFycnI0a9YsrVy5Uh0dHSopKZEkLVq0SGPHjpXP55Mk/eu//quWLVumjRs3KiMjQ83NzZKkESNGaMSIEeEoEYgcltX/7G9CGohqYQnqoqIiHT16VMuWLVNzc7OysrJUVVUVnGDW2NiomJhvTuZXr16trq4u/eM//mPIfioqKvTggw+Go0QgsvQV1oQ0EPXC8hz1UOM56rMQbc8Zf1s0jy+axwacYxx9jhoAANiHoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYHFOF2Acl+v0Nssa+joAABBn1KF6C+n+2gEACDOC+qQzhTFhDQBwAEEtDTyECWsAwBALW1BXVlYqIyNDCQkJys3N1Z49e/rs+8477+i///f/royMDLlcLq1cuTJcZQEAEFHCEtSbN2+W1+tVRUWF6uvrlZmZqYKCArW2tvba/4svvtDEiRO1YsUKpaamhqMkAAAiUliC+rHHHtMtt9yikpISTZ06VWvWrNHw4cP1zDPP9Np/5syZ+s1vfqOf/OQncrvd4SgJAICIZHtQd3V1qa6uTvn5+d8cJCZG+fn5qq2ttftwAABENdufoz527Ji6u7vl8XhC2j0ejw4cOGDLMTo7O9XZ2Rlc9/v9g9uhZQ1sohjPUwMAhlhEzvr2+XxKTk4OLunp6YPf6ZlCmJAGADjA9qAePXq0YmNj1dLSEtLe0tJi20Sx8vJytbW1BZempiZb9ttnGBPSAACH2B7U8fHxys7OVk1NTbAtEAiopqZGeXl5thzD7XYrKSkpZAkbQhoYGi7X6QuA8Lzr2+v1qri4WDk5OZo1a5ZWrlypjo4OlZSUSJIWLVqksWPHyufzSeqZgPbuu+8Gv/7000/V0NCgESNG6NJLLw1HiQBM0t/re/llGee4sAR1UVGRjh49qmXLlqm5uVlZWVmqqqoKTjBrbGxUTMw3J/NHjhzRjBkzguu//e1v9dvf/lbXXHONduzYEY4SAZhiIK/vJaxxDnNZVuT/H+D3+5WcnKy2trbBXwb/9j8akf+fJxTji1zROLazubwdDeMFvnY2uRWRs74BADhXENQAABiMoAYAwGAENQAABiOoAThnoBPEmEiGcxhBDcBZvL4X6BdBDcB5vL4X6BNBDcBMhDQgiaAGAMBoBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUADAUysokl+ubpazM6YoQIVyWZVlOFzFYfr9fycnJamtrU1JS0uB25nKFrkf+f55QjC9yRfPYpOge37fHdqpoGicG7GxyizNqAAin/kJ6IN/HOY+gBoBwGejlbS6Dox9c+v62aL78JjG+SBbNY5Oic3xnc7YcDePFgHHpGwCAKEFQAwBgMIIaAMLlzjvt7YdzEveovy0a75OdivFFrmgemxS94xvIfepoGSsGjHvUAGCKM4UwIY0zIKgBINx6C+M77ySkMSAENQAMhfPPD/368cedqwURhaAGAAze4cPSsGFSTEzPn4cPO11R1IhzugAAQISLjZUCgW/W//Y3aeLEntDu7naurijBGTUA4Lv7dkifKhDo+T4GJWxBXVlZqYyMDCUkJCg3N1d79uzpt/8LL7ygKVOmKCEhQVdccYVeffXVcJUGALDD4cN9h/RJgUDkXwbv6pJWrpTuuKPnz66uIT18WIJ68+bN8nq9qqioUH19vTIzM1VQUKDW1tZe++/atUsLFizQ4sWL9Ze//EWFhYUqLCzU/v37w1EeAMAOU6fa289E99wjDR8u3XWXtGpVz5/Dh/e0D5GwvPAkNzdXM2fO1KpVqyRJgUBA6enpuuOOO3Tfffed1r+oqEgdHR165ZVXgm3f//73lZWVpTVr1pzxeLzw5CwwvsgVzWOTon98I0ZIHR09X59/vnTihLP12CEmZmA/J5frzGfeJrrnHuk3v+n7+z//ufTII99p12eTW7ZPJuvq6lJdXZ3Ky8uDbTExMcrPz1dtbW2v29TW1srr9Ya0FRQUaOvWrXaXd0aWJOvUfzC++GLIawirb/9jyPgiRzSPTTo3xndyjC5XdIwvIaFn4thA+kXaeLu6pP/1v077e+myLAVbHntM+vWvpfj4sJZie1AfO3ZM3d3d8ng8Ie0ej0cHDhzodZvm5uZe+zc3N/fav7OzU52dncF1v98/yKq/YblcOnjZ5G8arsy2bd9GOHVsEuOLJNE8Nin6xzd2XOh6NIxv/ISB943E8V5y6WlNk98/KNfJqwjd3dKTT0pLl4a1jIic9e3z+ZScnBxc0tPT7dt5NFyOAgAMjQ8/DPshbD+jHj16tGJjY9XS0hLS3tLSotTU1F63SU1NPav+5eXlIZfK/X6/bWHtGjZMk+vrbNkXAJwTkpJ6vwcdEyPZeMVzSFVWSvfee1qz69v35C+5JOyl2B7U8fHxys7OVk1NjQoLCyX1TCarqanRkiVLet0mLy9PNTU1WnrK5YPq6mrl5eX12t/tdsvtdttduiTJ5XLJNXx4WPYNAFHpP/+z5xGsqVOlzk7J7ZbefVe6+GKnK/vuysqk8vL+X9gSGyvdfnvYSwnLpW+v16t169bp2Wef1XvvvafbbrtNHR0dKikpkSQtWrQoZLJZWVmZqqqq9Oijj+rAgQN68MEHtXfv3j6DHQBgmIsvlr78sufM+ssvIzukpZ4JYt+a5HwarzfsE8mkML1CtKioSEePHtWyZcvU3NysrKwsVVVVBSeMNTY2Kibmm98RZs+erY0bN+qBBx7Q/fffr0mTJmnr1q2aNm1aOMoDAODMTj569dhjoWfWsbE9If0dH806W2F5jnqo2focNQAAp+rq6pnd/eGHPfekb7990GfSjj5HDQBAVImPD/sjWP2JyMezAAA4V0TFGfXJq/d2vvgEAIBwOZlXA7n7HBVB3d7eLkn2vvgEAIAwa29vV3Jycr99omIyWSAQ0JEjR5SYmCjXt98X/B2cfIFKU1NTVE5OY3yRK5rHJjG+SBfN47N7bJZlqb29XWlpaSFPQfUmKs6oY2JiNG7cuDN3PEtJSUlR95ftVIwvckXz2CTGF+mieXx2ju1MZ9InMZkMAACDEdQAABiMoO6F2+1WRUVF2N4n7jTGF7mieWwS44t00Tw+J8cWFZPJAACIVpxRAwBgMIIaAACDEdQAABiMoP6WyspKZWRkKCEhQbm5udqzZ4/TJdnmzTff1Pz585WWliaXy6WtW7c6XZJtfD6fZs6cqcTERKWkpKiwsFAHDx50uizbrF69WtOnTw8+w5mXl6fXXnvN6bLCYsWKFXK5XFrq4Icg2O3BBx+Uy+UKWaZMmeJ0Wbb59NNP9dOf/lQXXnihhg0bpiuuuEJ79+51uixbZGRknPazc7lcKi0tHbIaCOpTbN68WV6vVxUVFaqvr1dmZqYKCgrU2trqdGm26OjoUGZmpiorK50uxXY7d+5UaWmpdu/ererqan311Ve67rrr1NHR4XRpthg3bpxWrFihuro67d27Vz/84Q91/fXX65133nG6NFu9/fbbeuqppzR9+nSnS7Hd9773PX322WfB5a233nK6JFt8/vnnmjNnjs477zy99tprevfdd/Xoo49q5MiRTpdmi7fffjvk51ZdXS1JuuGGG4auCAtBs2bNskpLS4Pr3d3dVlpamuXz+RysKjwkWVu2bHG6jLBpbW21JFk7d+50upSwGTlypPX73//e6TJs097ebk2aNMmqrq62rrnmGqusrMzpkmxTUVFhZWZmOl1GWNx7773WVVdd5XQZQ6asrMy65JJLrEAgMGTH5Iz6a11dXaqrq1N+fn6wLSYmRvn5+aqtrXWwMnwXbW1tkqRRo0Y5XIn9uru7tWnTJnV0dCgvL8/pcmxTWlqqefPmhfw/GE0++OADpaWlaeLEiVq4cKEaGxudLskWL7/8snJycnTDDTcoJSVFM2bM0Lp165wuKyy6urr03HPP6aabbrLlcyUGiqD+2rFjx9Td3S2PxxPS7vF41Nzc7FBV+C4CgYCWLl2qOXPmaNq0aU6XY5t9+/ZpxIgRcrvduvXWW7VlyxZNnTrV6bJssWnTJtXX18vn8zldSljk5uZqw4YNqqqq0urVq3X48GFdffXVwU/+i2QfffSRVq9erUmTJmnbtm267bbbdOedd+rZZ591ujTbbd26VcePH9eNN944pMeNig/lAE5VWlqq/fv3R809wJMmT56shoYGtbW16cUXX1RxcbF27twZ8WHd1NSksrIyVVdXKyEhwelywmLu3LnBr6dPn67c3FxNmDBBzz//vBYvXuxgZYMXCASUk5Oj5cuXS5JmzJih/fv3a82aNSouLna4Ons9/fTTmjt3rtLS0ob0uJxRf2306NGKjY1VS0tLSHtLS4tSU1Mdqgpna8mSJXrllVe0ffv2sHyimpPi4+N16aWXKjs7Wz6fT5mZmXr88cedLmvQ6urq1NraqiuvvFJxcXGKi4vTzp079cQTTyguLk7d3d1Ol2i7Cy64QJdddpkOHTrkdCmDNmbMmNN+Wbz88suj5tL+SR9//LHeeOMN3XzzzUN+bIL6a/Hx8crOzlZNTU2wLRAIqKamJqruA0Yry7K0ZMkSbdmyRX/+85918cUXO11S2AUCAXV2djpdxqBde+212rdvnxoaGoJLTk6OFi5cqIaGBsXGxjpdou1OnDihDz/8UGPGjHG6lEGbM2fOaY9Cvv/++5owYYJDFYXH+vXrlZKSonnz5g35sbn0fQqv16vi4mLl5ORo1qxZWrlypTo6OlRSUuJ0abY4ceJEyG/whw8fVkNDg0aNGqXx48c7WNnglZaWauPGjXrppZeUmJgYnFeQnJysYcOGOVzd4JWXl2vu3LkaP3682tvbtXHjRu3YsUPbtm1zurRBS0xMPG0uwfnnn68LL7wwauYY3H333Zo/f74mTJigI0eOqKKiQrGxsVqwYIHTpQ3aXXfdpdmzZ2v58uX68Y9/rD179mjt2rVau3at06XZJhAIaP369SouLlZcnAOxOWTzyyPE7373O2v8+PFWfHy8NWvWLGv37t1Ol2Sb7du3W5JOW4qLi50ubdB6G5cka/369U6XZoubbrrJmjBhghUfH29ddNFF1rXXXmu9/vrrTpcVNtH2eFZRUZE1ZswYKz4+3ho7dqxVVFRkHTp0yOmybPPHP/7RmjZtmuV2u60pU6ZYa9eudbokW23bts2SZB08eNCR4/PpWQAAGIx71AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAg8U5XYAdAoGAjhw5osTERLlcLqfLAQCgX5Zlqb29XWlpaYqJ6f+cOSqC+siRI0pPT3e6DAAAzkpTU5PGjRvXb5+oCOrExERJPQNOSkpyuBoAAPrn9/uVnp4ezK/+REVQn7zcnZSURFADACLGQG7XMpkMAACD2R7Ub775pubPn6+0tDS5XC5t3br1jNvs2LFDV155pdxuty699FJt2LDB7rIAAGF0+LA0bJgUE9Pz5+HDTldkn64uaeVK6Y47ev7s6hra49se1B0dHcrMzFRlZeWA+h8+fFjz5s3TD37wAzU0NGjp0qW6+eabtW3bNrtLAwDHlJVJLtc3S1mZ0xXZJzZWmjhR+tvfJMvq+XPixJ72SHfPPdLw4dJdd0mrVvX8OXx4T/tQcVmWZYVt5y6XtmzZosLCwj773HvvvfrTn/6k/fv3B9t+8pOf6Pjx46qqqhrQcfx+v5KTk9XW1sY9agDG6e82ZPj+BR4asbFSIND392NipO7uoavHTvfcI/3mN31//+c/lx555Lvt+2xyy/F71LW1tcrPzw9pKygoUG1trUMVAYB9zjRXKJJf/XD4cP8hLfV8PxIvg3d1SY891n+fxx4bmsvgjgd1c3OzPB5PSJvH45Hf79eXX37Z6zadnZ3y+/0hCwCYZqCXtyP1MvjUqfb2M8mTT575SkB3d0+/cHM8qL8Ln8+n5OTk4MLLTgCY6Ikn7O1nms5Oe/uZ5MMP7e03GI4HdWpqqlpaWkLaWlpalJSUpGHDhvW6TXl5udra2oJLU1PTUJQKIIxOnWh1coHZ3G57+5nkkkvs7TcYjgd1Xl6eampqQtqqq6uVl5fX5zZutzv4chNecgJEvr5CmbA227vv2tvPJLfffuZZ67GxPf3CzfagPnHihBoaGtTQ0CCp5/GrhoYGNTY2Suo5G160aFGw/6233qqPPvpI99xzjw4cOKAnn3xSzz//vO666y67SwNgoGiebHXnnfb2M83FF/fM6u5PTExPv0gTHy95vf338Xp7+oWdZbPt27dbkk5biouLLcuyrOLiYuuaa645bZusrCwrPj7emjhxorV+/fqzOmZbW5slyWpra7NnEACGRM/DSQNbIlU0j+2kmJjexxUT43Rlg/fzn58+vtjYnvbBOJvcCutz1EOF56iByHQ2Z8uR/C9VND9HfdKvfy398pc9X593nnTwYGSeSffmk0+kk3OWf/Ur6d57B38mHVHPUQNAtOstjO+8M3pCWpJSUr75etWq6AlpKTSU/+Vfhuhy9ykIagAYAuefH/r14487VwsiC0ENAIDBCGoAjhnopd9oukQMnC2CGoCjzhTChDTOdQQ1AMf1FcaENEBQAzAUIQ30IKgBADAYQQ0AgMEIagAADBbndAEABqa311ByHxeIfpxRAxGAj4EEzl0ENWC4aP4YSABnRlADBhtoCBPWQPQiqAEAMBhBDQCAwQhqAAAMRlADAGAwghowGB8DCYCgBgzHx0AC5zaCGogAfAwkcO4iqIEIRUgD5waCGgAAgxHUAAAYLGxBXVlZqYyMDCUkJCg3N1d79uzpt//KlSs1efJkDRs2TOnp6brrrrv0t7/9LVzlAQAQEcIS1Js3b5bX61VFRYXq6+uVmZmpgoICtba29tp/48aNuu+++1RRUaH33ntPTz/9tDZv3qz7778/HOUBABAxwhLUjz32mG655RaVlJRo6tSpWrNmjYYPH65nnnmm1/67du3SnDlz9E//9E/KyMjQddddpwULFpzxLBwAgGhne1B3dXWprq5O+fn53xwkJkb5+fmqra3tdZvZs2errq4uGMwfffSRXn31Vf3DP/xDr/07Ozvl9/tDFgAAolGc3Ts8duyYuru75fF4Qto9Ho8OHDjQ6zb/9E//pGPHjumqq66SZVn6z//8T9166619Xvr2+Xx66KGH7C4dAADjGDHre8eOHVq+fLmefPJJ1dfX6w9/+IP+9Kc/6eGHH+61f3l5udra2oJLU1PTEFcMAMDQsP2MevTo0YqNjVVLS0tIe0tLi1JTU3vd5pe//KX++Z//WTfffLMk6YorrlBHR4d+9rOf6Re/+IViYkJ/n3C73XK73XaXDgCAcWw/o46Pj1d2drZqamqCbYFAQDU1NcrLy+t1my+++OK0MI6NjZUkWbx+CQBwDrP9jFqSvF6viouLlZOTo1mzZmnlypXq6OhQSUmJJGnRokUaO3asfD6fJGn+/Pl67LHHNGPGDOXm5urQoUP65S9/qfnz5wcDGwCAc1FYgrqoqEhHjx7VsmXL1NzcrKysLFVVVQUnmDU2NoacQT/wwANyuVx64IEH9Omnn+qiiy7S/Pnz9T//5/8MR3kAAEQMlxUF15b9fr+Sk5PV1tampKQkp8sBwsLlCl2P/P9zQ0X7+EaMkDo6er4+/3zpxAln67Hb2rXSv/xLz9dPPSX97GfO1mOn1lbp5INMLS1SSsrg93k2uWXErG8AANA7ghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgsLC8QhRwyrffbiVF3xuuAJxbOKNG1OgtpPtrB4BIQFAjKpwpjAlrAJGKoEbEG2gIE9YAIhFBDQCAwQhqAAAMRlADAGAwghoAAIMR1Ih4A31OmuepAUQighpR4UwhTEgDiFQENaJGX2FMSAOIZAQ1ohohDSDSEdQAABiMoAYAwGBhC+rKykplZGQoISFBubm52rNnT7/9jx8/rtLSUo0ZM0Zut1uXXXaZXn311XCVBwBARAjLx1xu3rxZXq9Xa9asUW5urlauXKmCggIdPHhQKSkpp/Xv6urSj370I6WkpOjFF1/U2LFj9fHHH+uCCy4IR3kAAESMsAT1Y489pltuuUUlJSWSpDVr1uhPf/qTnnnmGd13332n9X/mmWf0H//xH9q1a5fOO+88SVJGRkY4SgMAIKLYfum7q6tLdXV1ys/P/+YgMTHKz89XbW1tr9u8/PLLysvLU2lpqTwej6ZNm6bly5eru7vb7vIAAIgotp9RHzt2TN3d3fJ4PCHtHo9HBw4c6HWbjz76SH/+85+1cOFCvfrqqzp06JBuv/12ffXVV6qoqDitf2dnpzo7O4Prfr/f3kEAAGAII2Z9BwIBpaSkaO3atcrOzlZRUZF+8YtfaM2aNb329/l8Sk5ODi7p6elDXDEAAEPD9qAePXq0YmNj1dLSEtLe0tKi1NTUXrcZM2aMLrvsMsXGxgbbLr/8cjU3N6urq+u0/uXl5WprawsuTU1N9g4CAABD2B7U8fHxys7OVk1NTbAtEAiopqZGeXl5vW4zZ84cHTp0SIFAINj2/vvva8yYMYqPjz+tv9vtVlJSUsgCAEA0Csulb6/Xq3Xr1unZZ5/Ve++9p9tuu00dHR3BWeCLFi1SeXl5sP9tt92m//iP/1BZWZnef/99/elPf9Ly5ctVWloajvIAAIgYYXk8q6ioSEePHtWyZcvU3NysrKwsVVVVBSeYNTY2Kibmm98R0tPTtW3bNt11112aPn26xo4dq7KyMt17773hKA8AgIgRlqCWpCVLlmjJkiW9fm/Hjh2nteXl5Wn37t3hKgcAgIhkxKxvAADQO4IaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADBa2oK6srFRGRoYSEhKUm5urPXv2DGi7TZs2yeVyqbCwMFylAQAQMcIS1Js3b5bX61VFRYXq6+uVmZmpgoICtba29rvdX//6V9199926+uqrw1EWAAARJyxB/dhjj+mWW25RSUmJpk6dqjVr1mj48OF65pln+tymu7tbCxcu1EMPPaSJEyeGoywAACKO7UHd1dWluro65efnf3OQmBjl5+ertra2z+1+9atfKSUlRYsXLz7jMTo7O+X3+0MWAACike1BfezYMXV3d8vj8YS0ezweNTc397rNW2+9paefflrr1q0b0DF8Pp+Sk5ODS3p6+qDrPle4XKcvAABzOT7ru729Xf/8z/+sdevWafTo0QPapry8XG1tbcGlqakpzFVGh75CmbAGAHPF2b3D0aNHKzY2Vi0tLSHtLS0tSk1NPa3/hx9+qL/+9a+aP39+sC0QCPQUFxengwcP6pJLLgnZxu12y+122116VDtTGLtckmUNTS0AgIGz/Yw6Pj5e2dnZqqmpCbYFAgHV1NQoLy/vtP5TpkzRvn371NDQEFz+63/9r/rBD36ghoYGLmvbYKBnzJxZA4B5bD+jliSv16vi4mLl5ORo1qxZWrlypTo6OlRSUiJJWrRokcaOHSufz6eEhARNmzYtZPsLLrhAkk5rBwDgXBOWoC4qKtLRo0e1bNkyNTc3KysrS1VVVcEJZo2NjYqJcfz2OAAAxgtLUEvSkiVLtGTJkl6/t2PHjn633bBhg/0FAQAQgTitBQDAYAT1OWCgs7mZ9Q0A5iGozxFnCmFCGgDMRFCfQ/oKY0IaAMxFUJ/jCGkAMBtBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAwWtqCurKxURkaGEhISlJubqz179vTZd926dbr66qs1cuRIjRw5Uvn5+f32BwDgXBGWoN68ebO8Xq8qKipUX1+vzMxMFRQUqLW1tdf+O3bs0IIFC7R9+3bV1tYqPT1d1113nT799NNwlAcAQMQIS1A/9thjuuWWW1RSUqKpU6dqzZo1Gj58uJ555ple+//v//2/dfvttysrK0tTpkzR73//ewUCAdXU1ISjPAAAIobtQd3V1aW6ujrl5+d/c5CYGOXn56u2tnZA+/jiiy/01VdfadSoUXaXBwBARImze4fHjh1Td3e3PB5PSLvH49GBAwcGtI97771XaWlpIWF/qs7OTnV2dgbX/X7/dy8YAACDGTfre8WKFdq0aZO2bNmihISEXvv4fD4lJycHl/T09CGuEgCAoWF7UI8ePVqxsbFqaWkJaW9paVFqamq/2/72t7/VihUr9Prrr2v69Ol99isvL1dbW1twaWpqsqV2AABMY3tQx8fHKzs7O2Qi2MmJYXl5eX1u98gjj+jhhx9WVVWVcnJy+j2G2+1WUlJSyAIAQDSy/R61JHm9XhUXFysnJ0ezZs3SypUr1dHRoZKSEknSokWLNHbsWPl8PknSv/7rv2rZsmXauHGjMjIy1NzcLEkaMWKERowYEY4SAQCICGEJ6qKiIh09elTLli1Tc3OzsrKyVFVVFZxg1tjYqJiYb07mV69era6uLv3jP/5jyH4qKir04IMPhqNEAAAiQliCWpKWLFmiJUuW9Pq9HTt2hKz/9a9/DVcZAABENONmfQMAgG8Q1AAAGIygBgDAYAQ1AAAGI6gBADBY2GZ9RyqX6/Q2yxr6OgAAkDijDtFbSPfXDgBAuBHUXztTGBPWAAAnENQaeAgT1gCAoUZQAwBgMIIaAACDEdQAABiMoAYAwGAEtQb+nDTPUwMAhhpB/bUzhTAhDQBwAkF9ir7CmJAGADiFoD4DQhoA4CSCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMFragrqysVEZGhhISEpSbm6s9e/b02/+FF17QlClTlJCQoCuuuEKvvvpquEoDACBihCWoN2/eLK/Xq4qKCtXX1yszM1MFBQVqbW3ttf+uXbu0YMECLV68WH/5y19UWFiowsJC7d+/PxzlAQAQMVyWZf+7t3JzczVz5kytWrVKkhQIBJSenq477rhD991332n9i4qK1NHRoVdeeSXY9v3vf19ZWVlas2bNGY/n9/uVnJystrY2JSUlDap2l8vSMNeXwfUTJwa1O+OMGBG6zvgiRzSPTYr+8aV4pC86er4efr7U2uJsPXZ7Zr105x09Xz/xO+mmEmfrsdPRo9LFF/d8ffizYfJ4XIPe59nklu1B3dXVpeHDh+vFF19UYWFhsL24uFjHjx/XSy+9dNo248ePl9fr1dKlS4NtFRUV2rp1q/7P//k/p/Xv7OxUZ2dncN3v9ys9Pd2WoB4e84XqLsse1D4AANFp1LY6eSYMH/R+ziaobb/0fezYMXV3d8vj8YS0ezweNTc397pNc3PzWfX3+XxKTk4OLunp6fYUr+j7LR4AYJ+LLhr6Y8YN/SEHr7y8XF6vN7h+8ozaDq5hwzS5vs6WfQEAootr2LAhP6btQT169GjFxsaqpSX0BkxLS4tSU1N73SY1NfWs+rvdbrndbnsK/haXyyXX8MFf1gAAwA62X/qOj49Xdna2ampqgm2BQEA1NTXKy8vrdZu8vLyQ/pJUXV3dZ38AAM4VYbn07fV6VVxcrJycHM2aNUsrV65UR0eHSkp6pgEuWrRIY8eOlc/nkySVlZXpmmuu0aOPPqp58+Zp06ZN2rt3r9auXRuO8gAAiBhhCeqioiIdPXpUy5YtU3Nzs7KyslRVVRWcMNbY2KiYmG9O5mfPnq2NGzfqgQce0P33369JkyZp69atmjZtWjjKAwAgYoTlOeqhZudz1AAAhJujj2cBAAD7ROTjWd928qKA3+93uBIAAM7sZF4N5KJ2VAR1e3u7JNn64hMAAMKtvb1dycnJ/faJinvUgUBAR44cUWJiolwue97Bmp6erqampqi85834Ilc0j01ifJEumsdn99gsy1J7e7vS0tJCJlf3JirOqGNiYjRu3Djb95uUlBR1f9lOxfgiVzSPTWJ8kS6ax2fn2M50Jn0Sk8kAADAYQQ0AgMEI6l643W5VVFSE7X3iTmN8kSuaxyYxvkgXzeNzcmxRMZkMAIBoxRk1AAAGI6gBADAYQQ0AgMEIagAADEZQf0tlZaUyMjKUkJCg3Nxc7dmzx+mSbPPmm29q/vz5SktLk8vl0tatW50uyTY+n08zZ85UYmKiUlJSVFhYqIMHDzpdlm1Wr16t6dOnB1+2kJeXp9dee83pssJixYoVcrlcWrp0qdOl2ObBBx+Uy+UKWaZMmeJ0Wbb59NNP9dOf/lQXXnihhg0bpiuuuEJ79+51uixbZGRknPazc7lcKi0tHbIaCOpTbN68WV6vVxUVFaqvr1dmZqYKCgrU2trqdGm26OjoUGZmpiorK50uxXY7d+5UaWmpdu/ererqan311Ve67rrr1NHR4XRpthg3bpxWrFihuro67d27Vz/84Q91/fXX65133nG6NFu9/fbbeuqppzR9+nSnS7Hd9773PX322WfB5a233nK6JFt8/vnnmjNnjs477zy99tprevfdd/Xoo49q5MiRTpdmi7fffjvk51ZdXS1JuuGGG4auCAtBs2bNskpLS4Pr3d3dVlpamuXz+RysKjwkWVu2bHG6jLBpbW21JFk7d+50upSwGTlypPX73//e6TJs097ebk2aNMmqrq62rrnmGqusrMzpkmxTUVFhZWZmOl1GWNx7773WVVdd5XQZQ6asrMy65JJLrEAgMGTH5Iz6a11dXaqrq1N+fn6wLSYmRvn5+aqtrXWwMnwXbW1tkqRRo0Y5XIn9uru7tWnTJnV0dCgvL8/pcmxTWlqqefPmhfw/GE0++OADpaWlaeLEiVq4cKEaGxudLskWL7/8snJycnTDDTcoJSVFM2bM0Lp165wuKyy6urr03HPP6aabbrLlA6AGiqD+2rFjx9Td3S2PxxPS7vF41Nzc7FBV+C4CgYCWLl2qOXPmaNq0aU6XY5t9+/ZpxIgRcrvduvXWW7VlyxZNnTrV6bJssWnTJtXX18vn8zldSljk5uZqw4YNqqqq0urVq3X48GFdffXVwY/ojWQfffSRVq9erUmTJmnbtm267bbbdOedd+rZZ591ujTbbd26VcePH9eNN944pMeNik/PAk5VWlqq/fv3R809wJMmT56shoYGtbW16cUXX1RxcbF27twZ8WHd1NSksrIyVVdXKyEhwelywmLu3LnBr6dPn67c3FxNmDBBzz//vBYvXuxgZYMXCASUk5Oj5cuXS5JmzJih/fv3a82aNSouLna4Ons9/fTTmjt3rtLS0ob0uJxRf2306NGKjY1VS0tLSHtLS4tSU1Mdqgpna8mSJXrllVe0ffv2sHz0qZPi4+N16aWXKjs7Wz6fT5mZmXr88cedLmvQ6urq1NraqiuvvFJxcXGKi4vTzp079cQTTyguLk7d3d1Ol2i7Cy64QJdddpkOHTrkdCmDNmbMmNN+Wbz88suj5tL+SR9//LHeeOMN3XzzzUN+bIL6a/Hx8crOzlZNTU2wLRAIqKamJqruA0Yry7K0ZMkSbdmyRX/+85918cUXO11S2AUCAXV2djpdxqBde+212rdvnxoaGoJLTk6OFi5cqIaGBsXGxjpdou1OnDihDz/8UGPGjHG6lEGbM2fOaY9Cvv/++5owYYJDFYXH+vXrlZKSonnz5g35sbn0fQqv16vi4mLl5ORo1qxZWrlypTo6OlRSUuJ0abY4ceJEyG/whw8fVkNDg0aNGqXx48c7WNnglZaWauPGjXrppZeUmJgYnFeQnJysYcOGOVzd4JWXl2vu3LkaP3682tvbtXHjRu3YsUPbtm1zurRBS0xMPG0uwfnnn68LL7wwauYY3H333Zo/f74mTJigI0eOqKKiQrGxsVqwYIHTpQ3aXXfdpdmzZ2v58uX68Y9/rD179mjt2rVau3at06XZJhAIaP369SouLlZcnAOxOWTzyyPE7373O2v8+PFWfHy8NWvWLGv37t1Ol2Sb7du3W5JOW4qLi50ubdB6G5cka/369U6XZoubbrrJmjBhghUfH29ddNFF1rXXXmu9/vrrTpcVNtH2eFZRUZE1ZswYKz4+3ho7dqxVVFRkHTp0yOmybPPHP/7RmjZtmuV2u60pU6ZYa9eudbokW23bts2SZB08eNCR4/MxlwAAGIx71AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAg8U5XYAdAoGAjhw5osTERLlcLqfLAQCgX5Zlqb29XWlpaYqJ6f+cOSqC+siRI0pPT3e6DAAAzkpTU5PGjRvXb5+oCOrExERJPQNOSkpyuBoAAPrn9/uVnp4ezK/+REVQn7zcnZSURFADACLGQG7XRkVQY+BcD53+l8KqsByoBAAwEGc96/vNN9/U/PnzlZaWJpfLpa1bt4Z837IsLVu2TGPGjNGwYcOUn5+vDz744Iz7raysVEZGhhISEpSbm6s9e/acbWk4g95Cur92AIDzzjqoOzo6lJmZqcrKyl6//8gjj+iJJ57QmjVr9O///u86//zzVVBQoL/97W997nPz5s3yer2qqKhQfX29MjMzVVBQoNbW1rMtD304UxgT1gBgJpdlWd/5uqfL5dKWLVtUWFgoqedsOi0tTf/jf/wP3X333ZKktrY2eTwebdiwQT/5yU963U9ubq5mzpypVatWSep53Co9PV133HGH7rvvvjPW4ff7lZycrLa2Nu5R9+JsQpjL4AAQfmeTW7a+8OTw4cNqbm5Wfn5+sC05OVm5ubmqra3tdZuuri7V1dWFbBMTE6P8/Pw+t+ns7JTf7w9ZAACIRrYGdXNzsyTJ4/GEtHs8nuD3vu3YsWPq7u4+q218Pp+Sk5ODC89QAwCiVUS+QrS8vFxtbW3BpampyemSAAAIC1uDOjU1VZLU0tIS0t7S0hL83reNHj1asbGxZ7WN2+0OPjPNs9MAgGhma1BffPHFSk1NVU1NTbDN7/fr3//935WXl9frNvHx8crOzg7ZJhAIqKamps9tcHYGOkGMiWQAYJ6zDuoTJ06ooaFBDQ0NknomkDU0NKixsVEul0tLly7Vr3/9a7388svat2+fFi1apLS0tODMcEm69tprgzO8Jcnr9WrdunV69tln9d577+m2225TR0eHSkpKBj1A9DhTCBPSAGCms34z2d69e/WDH/wguO71eiVJxcXF2rBhg+655x51dHToZz/7mY4fP66rrrpKVVVVSkhICG7z4Ycf6tixY8H1oqIiHT16VMuWLVNzc7OysrJUVVV12gQzDI5VYfFmMgCIMIN6jtoUPEc9cN8OakIaAIaeY89RAwAAexHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAazPagzMjLkcrlOW0pLS3vtv2HDhtP6JiQk2F0WAAARKc7uHb799tvq7u4Oru/fv18/+tGPdMMNN/S5TVJSkg4ePBhcd7lcdpcFAEBEsj2oL7roopD1FStW6JJLLtE111zT5zYul0upqal2lwIAQMQL6z3qrq4uPffcc7rpppv6PUs+ceKEJkyYoPT0dF1//fV65513+t1vZ2en/H5/yAIAQDQKa1Bv3bpVx48f14033thnn8mTJ+uZZ57RSy+9pOeee06BQECzZ8/WJ5980uc2Pp9PycnJwSU9PT0M1QMA4DyXZVlWuHZeUFCg+Ph4/fGPfxzwNl999ZUuv/xyLViwQA8//HCvfTo7O9XZ2Rlc9/v9Sk9PV1tbm5KSkgZddzRzPRR6ZcOqCNuPHwDQB7/fr+Tk5AHllu33qE/6+OOP9cYbb+gPf/jDWW133nnnacaMGTp06FCffdxut9xu92BLBADAeGG79L1+/XqlpKRo3rx5Z7Vdd3e39u3bpzFjxoSpMgAAIkdYgjoQCGj9+vUqLi5WXFzoSfuiRYtUXl4eXP/Vr36l119/XR999JHq6+v105/+VB9//LFuvvnmcJQGAEBECcul7zfeeEONjY266aabTvteY2OjYmK++f3g888/1y233KLm5maNHDlS2dnZ2rVrl6ZOnRqO0gAAiChhnUw2VM7mpvy5jslkAOC8s8kt3vUNAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAg9ke1A8++KBcLlfIMmXKlH63eeGFFzRlyhQlJCToiiuu0Kuvvmp3WQAARKSwnFF/73vf02effRZc3nrrrT777tq1SwsWLNDixYv1l7/8RYWFhSosLNT+/fvDURoAABElLEEdFxen1NTU4DJ69Og++z7++OP6L//lv+jnP/+5Lr/8cj388MO68sortWrVqnCUBgBARAlLUH/wwQdKS0vTxIkTtXDhQjU2NvbZt7a2Vvn5+SFtBQUFqq2tDUdpAABElDi7d5ibm6sNGzZo8uTJ+uyzz/TQQw/p6quv1v79+5WYmHha/+bmZnk8npA2j8ej5ubmPo/R2dmpzs7O4Lrf77dvAAAAGMT2oJ47d27w6+nTpys3N1cTJkzQ888/r8WLF9tyDJ/Pp4ceesiWfQEAYLKwP551wQUX6LLLLtOhQ4d6/X5qaqpaWlpC2lpaWpSamtrnPsvLy9XW1hZcmpqabK0ZAABThD2oT5w4oQ8//FBjxozp9ft5eXmqqakJaauurlZeXl6f+3S73UpKSgpZAACIRrYH9d13362dO3fqr3/9q3bt2qX/9t/+m2JjY7VgwQJJ0qJFi1ReXh7sX1ZWpqqqKj366KM6cOCAHnzwQe3du1dLliyxuzQAACKO7feoP/nkEy1YsED/7//9P1100UW66qqrtHv3bl100UWSpMbGRsXEfPP7wezZs7Vx40Y98MADuv/++zVp0iRt3bpV06ZNs7s0AAAijsuyLMvpIgbL7/crOTlZbW1tXAY/A9dDrpB1qyLif/wAEHHOJrd41zcAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMZntQ+3w+zZw5U4mJiUpJSVFhYaEOHjzY7zYbNmyQy+UKWRISEuwuDQCAiGN7UO/cuVOlpaXavXu3qqur9dVXX+m6665TR0dHv9slJSXps88+Cy4ff/yx3aUBABBx4uzeYVVVVcj6hg0blJKSorq6Ov3d3/1dn9u5XC6lpqbaXQ4AABEt7Peo29raJEmjRo3qt9+JEyc0YcIEpaen6/rrr9c777wT7tIAADBeWIM6EAho6dKlmjNnjqZNm9Znv8mTJ+uZZ57RSy+9pOeee06BQECzZ8/WJ5980mv/zs5O+f3+kAUAgGhk+6XvU5WWlmr//v166623+u2Xl5envLy84Prs2bN1+eWX66mnntLDDz98Wn+fz6eHHnrI9noBADBN2M6olyxZoldeeUXbt2/XuHHjzmrb8847TzNmzNChQ4d6/X55ebna2tqCS1NTkx0lAwBgHNvPqC3L0h133KEtW7Zox44duvjii896H93d3dq3b5/+4R/+odfvu91uud3uwZYKAIDxbA/q0tJSbdy4US+99JISExPV3NwsSUpOTtawYcMkSYsWLdLYsWPl8/kkSb/61a/0/e9/X5deeqmOHz+u3/zmN/r444918803210eAAARxfagXr16tSTp7//+70Pa169frxtvvFGS1NjYqJiYb666f/7557rlllvU3NyskSNHKjs7W7t27dLUqVPtLg8AgIjisizLcrqIwfL7/UpOTlZbW5uSkpKcLsdorodcIetWRcT/+AEg4pxNbvGubwAADEZQAwBgMIIaAACDEdQAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMBhBDQCAwQhqAAAMRlADAGAwghoAAIMR1AAAGIygBgDAYAQ1AAAGI6gBADAYQQ0AgMEIagAADEZQAwBgMIIaAACDEdQAABgsbEFdWVmpjIwMJSQkKDc3V3v27Om3/wsvvKApU6YoISFBV1xxhV599dVwlQYAQMQIS1Bv3rxZXq9XFRUVqq+vV2ZmpgoKCtTa2tpr/127dmnBggVavHix/vKXv6iwsFCFhYXav39/OMoDACBiuCzLsuzeaW5urmbOnKlVq1ZJkgKBgNLT03XHHXfovvvuO61/UVGROjo69MorrwTbvv/97ysrK0tr1qw54/H8fr+Sk5PV1tampKQk+wYShVwPuULWrQrbf/wAgDM4m9yKs/vgXV1dqqurU3l5ebAtJiZG+fn5qq2t7XWb2tpaeb3ekLaCggJt3brV7vLOyLIsWV9+OeTHHSrD/jM0qANffOFQJQAQeVzDhsnlcp25o41sD+pjx46pu7tbHo8npN3j8ejAgQO9btPc3Nxr/+bm5l77d3Z2qrOzM7ju9/sHWfU3rC+/1MErs23bn2nqNDlk/eAL0TtWALDb5Po6uYYPH9JjRuSsb5/Pp+Tk5OCSnp5u275H+EbYti8AAAbL9jPq0aNHKzY2Vi0tLSHtLS0tSk1N7XWb1NTUs+pfXl4ecqnc7/fbFtZfxlrKvuFgcP1E+Qlb9gsAiHyuYcOG/Ji2B3V8fLyys7NVU1OjwsJCST2TyWpqarRkyZJet8nLy1NNTY2WLl0abKuurlZeXl6v/d1ut9xut92l93BJX8Z9M8EqZogvcQAAcCrbg1qSvF6viouLlZOTo1mzZmnlypXq6OhQSUmJJGnRokUaO3asfD6fJKmsrEzXXHONHn30Uc2bN0+bNm3S3r17tXbt2nCUBwBAxAhLUBcVFeno0aNatmyZmpublZWVpaqqquCEscbGRsXEfHN7fPbs2dq4caMeeOAB3X///Zo0aZK2bt2qadOmhaM8AAAiRlieox5qdj5HzXPGAIBwO5vcishZ3wAAnCsIagAADEZQAwBgMIIaAACDEdQAABiMoD6Db88CBwBgKBHUp+grlAlrAIBTCOqvnSmMCWsAgBMIag08hAlrAMBQI6gBADAYQQ0AgMEIagAADEZQAwBgMIJaA/+ELD5JCwAw1Ajqr50phAlpAIATCOpT9BXGhDQAwClxThdgGkIZAGCSqAhqy+oJV7/f73AlAACc2cm8Oplf/YmKoG5vb5ckpaenO1wJAAAD197eruTk5H77uKyBxLnhAoGAjhw5osTERLlcg3/Np9/vV3p6upqampSUlGRDhWZhfJErmscmMb5IF83js3tslmWpvb1daWlpionpf7pYVJxRx8TEaNy4cbbvNykpKer+sp2K8UWuaB6bxPgiXTSPz86xnelM+iRmfQMAYDCCGgAAgxHUvXC73aqoqJDb7Xa6lLBgfJErmscmMb5IF83jc3JsUTGZDACAaMUZNQAABiOoAQAwGEENAIDBCGoAAAxGUH9LZWWlMjIylJCQoNzcXO3Zs8fpkmzz5ptvav78+UpLS5PL5dLWrVudLsk2Pp9PM2fOVGJiolJSUlRYWKiDBw86XZZtVq9erenTpwdftpCXl6fXXnvN6bLCYsWKFXK5XFq6dKnTpdjmwQcflMvlClmmTJnidFm2+fTTT/XTn/5UF154oYYNG6YrrrhCe/fudbosW2RkZJz2s3O5XCotLR2yGgjqU2zevFler1cVFRWqr69XZmamCgoK1Nra6nRptujo6FBmZqYqKyudLsV2O3fuVGlpqXbv3q3q6mp99dVXuu6669TR0eF0abYYN26cVqxYobq6Ou3du1c//OEPdf311+udd95xujRbvf3223rqqac0ffp0p0ux3fe+9z199tlnweWtt95yuiRbfP7555ozZ47OO+88vfbaa3r33Xf16KOPauTIkU6XZou333475OdWXV0tSbrhhhuGrggLQbNmzbJKS0uD693d3VZaWprl8/kcrCo8JFlbtmxxuoywaW1ttSRZO3fudLqUsBk5cqT1+9//3ukybNPe3m5NmjTJqq6utq655hqrrKzM6ZJsU1FRYWVmZjpdRljce++91lVXXeV0GUOmrKzMuuSSS6xAIDBkx+SM+mtdXV2qq6tTfn5+sC0mJkb5+fmqra11sDJ8F21tbZKkUaNGOVyJ/bq7u7Vp0yZ1dHQoLy/P6XJsU1paqnnz5oX8PxhNPvjgA6WlpWnixIlauHChGhsbnS7JFi+//LJycnJ0ww03KCUlRTNmzNC6deucLissurq69Nxzz+mmm26y5QOgBoqg/tqxY8fU3d0tj8cT0u7xeNTc3OxQVfguAoGAli5dqjlz5mjatGlOl2Obffv2acSIEXK73br11lu1ZcsWTZ061emybLFp0ybV19fL5/M5XUpY5ObmasOGDaqqqtLq1at1+PBhXX311cGP6I1kH330kVavXq1JkyZp27Ztuu2223TnnXfq2Wefdbo0223dulXHjx/XjTfeOKTHjYpPzwJOVVpaqv3790fNPcCTJk+erIaGBrW1tenFF19UcXGxdu7cGfFh3dTUpLKyMlVXVyshIcHpcsJi7ty5wa+nT5+u3NxcTZgwQc8//7wWL17sYGWDFwgElJOTo+XLl0uSZsyYof3792vNmjUqLi52uDp7Pf3005o7d67S0tKG9LicUX9t9OjRio2NVUtLS0h7S0uLUlNTHaoKZ2vJkiV65ZVXtH379rB89KmT4uPjdemllyo7O1s+n0+ZmZl6/PHHnS5r0Orq6tTa2qorr7xScXFxiouL086dO/XEE08oLi5O3d3dTpdouwsuuECXXXaZDh065HQpgzZmzJjTflm8/PLLo+bS/kkff/yx3njjDd18881DfmyC+mvx8fHKzs5WTU1NsC0QCKimpiaq7gNGK8uytGTJEm3ZskV//vOfdfHFFztdUtgFAgF1dnY6XcagXXvttdq3b58aGhqCS05OjhYuXKiGhgbFxsY6XaLtTpw4oQ8//FBjxoxxupRBmzNnzmmPQr7//vuaMGGCQxWFx/r165WSkqJ58+YN+bG59H0Kr9er4uJi5eTkaNasWVq5cqU6OjpUUlLidGm2OHHiRMhv8IcPH1ZDQ4NGjRql8ePHO1jZ4JWWlmrjxo166aWXlJiYGJxXkJycrGHDhjlc3eCVl5dr7ty5Gj9+vNrb27Vx40bt2LFD27Ztc7q0QUtMTDxtLsH555+vCy+8MGrmGNx9992aP3++JkyYoCNHjqiiokKxsbFasGCB06UN2l133aXZs2dr+fLl+vGPf6w9e/Zo7dq1Wrt2rdOl2SYQCGj9+vUqLi5WXJwDsTlk88sjxO9+9ztr/PjxVnx8vDVr1ixr9+7dTpdkm+3bt1uSTluKi4udLm3QehuXJGv9+vVOl2aLm266yZowYYIVHx9vXXTRRda1115rvf76606XFTbR9nhWUVGRNWbMGCs+Pt4aO3asVVRUZB06dMjpsmzzxz/+0Zo2bZrldrutKVOmWGvXrnW6JFtt27bNkmQdPHjQkePzMZcAABiMe9QAABiMoAYAwGAENQAABiOoAQAwGEENAIDBCGoAAAxGUAMAYDCCGgAAgxHUAAAYjKAGAMBgBDUAAAYjqAEAMNj/B/oXX+GEjuitAAAAAElFTkSuQmCC","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":13,"id":"98d5f012","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["prob that a norm(0,1) takes a value of 0.5: 0.3520653267642995\n","prob that uniform(0,1) takes vales less than 0.3: 0.3\n"]}],"source":["# TODO\n","from scipy.stats import norm, uniform\n","\n","def dnorm(x,mean=0,sd=1):\n"," result= norm.pdf(x, loc=mean , scale=sd)\n"," return result\n","\n","def pnorm(q, mean = 0,sd =1):\n"," result= norm.cdf(q,loc=mean, scale=sd)\n"," return result \n","\n","def qnorm(p,mean=0, sd=1):\n"," result=norm.ppf(p, loc=mean,scale=sd)\n"," return result \n","\n","def rnorm(n, mean=0, sd=1):\n"," result=norm.rvs(loc=mean,scale=sd,size=n)\n"," return result\n","\n","def dunif(x,low=0,high=1):\n"," result= uniform.pdf(x,loc=low,scale=high-low)\n"," return result \n","\n","def punif(q, low=0,high = 1):\n"," result=uniform.cdf(q,loc=low,scale=high -low)\n"," return result\n","\n","def qunif(p,low=0, high=1):\n"," result=uniform.ppf(p,loc=low, scale=high - low )\n"," return result \n","\n","def runif(n,low=0,high=1):\n"," result = uniform.rvs(loc=low,scale=high - low, size=n)\n"," return result \n","\n","\n","print(f\"prob that a norm(0,1) takes a value of 0.5: {dnorm(0.5)}\")\n","print(f\"prob that uniform(0,1) takes vales less than 0.3: {punif(0.3)}\")\n","\n"]},{"cell_type":"code","execution_count":12,"id":"05d20cee","metadata":{},"outputs":[{"data":{"image/png":"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"]},"metadata":{},"output_type":"display_data"}],"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","x_uniform=np.linspace(0,1,1000)\n","x_normal=np.linspace(-5, 5, 1000)\n","\n","pdf_uniform=dunif(x_uniform)\n","cdf_uniform=punif(x_uniform)\n","\n","pdf_normal=dnorm(x_normal)\n","cdf_normal=pnorm(x_normal)\n","\n","fig, axes = plt.subplots(2,2 , figsize=(12,10))\n","\n","\n","axes[0, 0].plot(x_uniform, pdf_uniform, label=\"uniform pdf\")\n","axes[0, 0].set_title('uniform distribution - pdf')\n","axes[0, 0].set_xlabel('x')\n","axes[0, 0].set_ylabel('probability density')\n","axes[0, 0].legend()\n","\n","axes[0, 1].plot(x_uniform, cdf_uniform, label=\"uniform cdf\")\n","axes[0, 1].set_title('uniform distribution - cdf')\n","axes[0, 1].set_xlabel('x')\n","axes[0, 1].set_ylabel('cumulative probability')\n","axes[0, 1].legend()\n","\n","axes[1, 0].plot(x_normal, pdf_normal, label=\"normal pdf\")\n","axes[1, 0].set_title('normal distribution - pdf')\n","axes[1, 0].set_xlabel('x')\n","axes[1, 0].set_ylabel('probability density')\n","axes[1, 0].legend()\n","\n","axes[1, 1].plot(x_normal, cdf_normal, label=\"normal cdf\")\n","axes[1, 1].set_title('normal distribution - cdf')\n","axes[1, 1].set_xlabel('x')\n","axes[1, 1].set_ylabel('cumulative probability')\n","axes[1, 1].legend()\n","\n","plt.tight_layout()\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/Rashid/problems.ipynb b/Rashid/problems.ipynb new file mode 100644 index 00000000..be9d53ec --- /dev/null +++ b/Rashid/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":2,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":3,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":6,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":4,"id":"98d5f012","metadata":{},"outputs":[],"source":["# TODO\n","\n","from scipy.stats import norm\n","# Normal Distributions\n","\n","def normpdf(x, mean, std):\n"," return norm.pdf(x, loc = mean, scale = std)\n","\n","def normcdf(x, mean, std):\n"," return norm.cdf(x, loc = mean, scale = std)\n","\n","def normppf(p, mean, std):\n"," return norm.ppf(p, loc = mean, scale = std)\n","\n","def normrvs(n, mean, std):\n"," return norm.rvs(loc = mean, scale = std, size = n)\n"]},{"cell_type":"code","execution_count":8,"id":"6dfff0d2","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["np.random.seed(42)\n","\n","mean = 10\n","standard_deviation = 2\n","data = normrvs(2000, mean, standard_deviation)\n","\n","pdf = normpdf(data, mean = mean, std = standard_deviation)\n","cdf = normcdf(data, mean = mean, std = standard_deviation)\n","ppf = normppf(data, mean = mean, std = standard_deviation)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pdf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"code","execution_count":16,"id":"3b71f718","metadata":{},"outputs":[],"source":["from scipy.stats import uniform \n","# Uniform Distributions\n","\n","def unipdf(x, low, high):\n"," return uniform.pdf(x, loc = low, scale = (high - low))\n","\n","def unicdf(x, low, high):\n"," return uniform.cdf(x, loc = low, scale = (high - low))\n","\n","def unippf(q, low, high):\n"," return uniform.ppf(q, loc = low, scale = (high - low))\n","\n","def unirvs(n, low, high):\n"," return uniform.rvs(low, high - low, size=n)"]},{"cell_type":"code","execution_count":18,"id":"55729c79","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["np.random.seed(42)\n","\n","low = 10\n","high = 30\n","data = unirvs(2000, low = low, high = high)\n","\n","pdf = unipdf(data, low = low, high = high)\n","cdf = unicdf(data, low = low, high = high)\n","ppf = unippf(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pdf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"code","execution_count":null,"id":"a993c4e0","metadata":{},"outputs":[],"source":[]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/Ricardo/problems.ipynb b/Ricardo/problems.ipynb new file mode 100644 index 00000000..5d516df2 --- /dev/null +++ b/Ricardo/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":3,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":4,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":5,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":28,"id":"98d5f012","metadata":{},"outputs":[],"source":["from scipy.stats import norm\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n","\n"," result = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n","\n"," result = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result\n","\n","def qnorm(p, mean = 0, std = 1):\n","\n"," result = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result\n","\n","def rnorm(n, mean = 0, std = 1):\n","\n"," result = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result"]},{"cell_type":"code","execution_count":29,"id":"fab0f876","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","std = 2\n","mean = .5\n","data = rnorm(2000, mean = 0, std = 1)\n","\n","pdf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pdf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"code","execution_count":30,"id":"177cc032","metadata":{},"outputs":[],"source":["from scipy.stats import uniform\n","\n","#Uniforme\n","def dunif(x, low = 0, high = 1):\n","\n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def punif(q, low = 0, high = 1):\n","\n"," result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def qunif(p, low = 0, high = 1):\n","\n"," result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def runif(n, low = 0, high = 1):\n","\n"," result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":31,"id":"63256657","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","high = .9\n","low = .1\n","data = runif(2000, low = 0, high = 1)\n","\n","pdf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pdf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/Rob/problems.ipynb b/Rob/problems.ipynb new file mode 100644 index 00000000..9b9ad7b3 --- /dev/null +++ b/Rob/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":2,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":3,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":4,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":1,"id":"98d5f012","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["#Normal Distribution \n","from scipy.stats import norm\n","import numpy as np\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n","\n"," result = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n","\n"," result = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result\n","\n","def qnorm(p, mean = 0, std = 1):\n","\n"," result = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result\n","\n","def rnorm(n, mean = 0, std = 1):\n","\n"," result = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result\n","\n","\n","\n","\n","import matplotlib.pyplot as plt\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()\n","\n"]},{"cell_type":"code","execution_count":2,"id":"a2ea5ac2","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["#Uniform \n","from scipy.stats import uniform \n","import numpy as np \n","\n","\n","\n","def dunif(x, low = 0, high = 1):\n","\n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def punif(q, low = 0, high = 1):\n","\n"," result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def qunif(p, low = 0, high = 1):\n","\n"," result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def runif(n, low = 0, high = 1):\n","\n"," result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n"," return result\n","\n","\n","np.random.seed(42)\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/SethK/problems.ipynb b/SethK/problems.ipynb new file mode 100644 index 00000000..096d3611 --- /dev/null +++ b/SethK/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":6,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":7,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":8,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":9,"id":"98d5f012","metadata":{},"outputs":[],"source":["from scipy.stats import norm\n","import matplotlib.pyplot as plt\n","import numpy as np\n","\n","# Define all the probability functions related to this distribution\n","#The normal distribution isn't the same steps, but seems simimllar to the binomial distribution steps. \n","\n","def densnorm(x, mean = 0, std = 1):\n"," \n"," #pdf will help measure density\n"," #Calculates the density of the normal distribution\n"," \n"," result1 = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result1\n","\n","def pnorm(x, mean = 0, std = 1):\n"," \n"," #cdf will return cumlative distribution\n"," #Calculates the cumulative of the normal distribution\n"," \n"," result2 = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result2\n","\n","def quantilenorm(p, mean = 0, std = 1):\n"," \n"," #Calculates the quantile function from the normal distribution\n"," \n"," result3 = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result3\n","\n","def randnorm(n, mean = 0, std = 1):\n"," \n"," #Generates random variables from the normal distribution\n"," \n"," result4 = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result4"]},{"cell_type":"code","execution_count":10,"id":"a7aedd6a","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["#Show the distribution in plots\n","np.random.seed(42)\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01) #-5 starting point, 5 ending point, 0.01 is the spacing as we see on the y axis\n","\n","pmf = densnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = quantilenorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\") #r stands for red\n","axis[1].plot(data, cdf, \"b-\") #b stands for blue\n","axis[2].plot(data, ppf, \"g-\") #g stands for green\n","\n","# Makes the layout of the graph neater\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"code","execution_count":14,"id":"e6e54e34","metadata":{},"outputs":[],"source":["from scipy.stats import uniform\n","\n","#Uniform distribution\n","def pointif(x, low = 0, high = 1):\n"," \n"," #Will find the point estimate of the uniform distribution\n"," \n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def cumlif(q, low = 0, high = 1):\n"," \n"," #Will find the cumulative of the uniform distribution\n"," \n"," result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def quanif(p, low = 0, high = 1):\n"," \n"," #Will fint the quantile function from the uniform distribution\n"," \n"," result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def randif(n, low = 0, high = 1):\n"," \n"," #Will generate random variables from the uniform distribution\n"," \n"," result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":16,"id":"b38efd00","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["#Show the distributions in plots\n","\n","np.random.seed(42)\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = pointif(data, low = low, high = high)\n","cdf = cumlif(data, low = low, high = high)\n","ppf = quanif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/examples.ipynb b/examples.ipynb new file mode 100644 index 00000000..d2a2c07b --- /dev/null +++ b/examples.ipynb @@ -0,0 +1,332 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Random Variables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Definition.** Let e be an experiment and $\\mathcal{S}$ a sample space associated with the experiment. A function $X$ assigning to every element $s \\in \\mathcal{S}$, a real number, $X(s)$, is called a random variable." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Example 1:** Consider the following random variable generated by a dice $\\mathcal{S}=\\{1,2,3,4,5,6\\}$:\n", + "- $X=+\\$3$ if $s=\\{1,2\\}$\n", + "- $X=-\\$2$ if $s=\\{3,4\\}$\n", + "- $X=+\\$1$ if $s=\\{5\\}$\n", + "- $X=-\\$4$ if $s=\\{6\\}$\n", + " \n", + "1. Compute the expectation (mean) of $X$.\n", + "2. Compute the variance of $X$. \n", + "3. Plot the distribution of this random variable." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+X/5NSmhoqKRLw7Eu31Z++dXef0l66KGHdOjQIZthVsuXL5eTk5Puv/9+SZfG0+ffE5CXl6dTp04pJydHbdu2LfQ16tu3r3UIT3Euf90vXLigEydOqEOHDpJUaLuPP/64zfOxY8dKUrGfxw8//FCdO3eWl5eXzbEUFham3NzcAsPLiuLk5CRPT09J0t13313h9xfAvgi8MJX58+fr66+/1tq1a7V9+3b997//LfAPUrVq1XTjjTfalO3fv1/+/v6qUaOGTXn+V7z5/2jna9y4cYFt33TTTTp37px13OL58+c1efJk6xgzb29v+fj4KC0tTenp6QXWv7JNd3d31a1bt0LnrG3atKnatWund99911r27rvvqkOHDgoODr7m9s+ePVvgNb1cly5d1LdvX02dOlXe3t7q1auXFi1aVGCsY3EKez+LU9R7V9FzA+/fv18ODg4FXlc/Pz/VrFmzwDF2edjJ5+XlVWBcd2HbKc2xXF6u7G/+EIP8/u7evVvSpSDn4+Nj81izZo2OHTtWou1MnjxZX3/9tT755BMNHjxY6enphX7F//nnn6tDhw5ycXFRrVq1rENQCvvsXe21Pn78uM6fP1/osdOkSROb59f6PucHsICAgELLr/b+S9KAAQPk6Ohona3hwoUL+uSTT9S9e3eboR9LlixRy5Yt5eLiotq1a8vHx0dffPFFoa9Rw4YNr7pdSTp16pSeeOIJ+fr6ytXVVT4+PtZ1S3LeCwoKkoODQ7Gfx927dyshIaHAcRQWFiZJJT6WXnnlFf32229q3ry55s6dW+x0brj+MYYXptK+fXvrLA1FcXZ2LnYMXHkZO3asFi1apCeffFIdO3aUp6enLBaLBgwYUKIbKyrL4MGD9cQTT+jQoUPKysrS+vXrbW40K6uLFy/qzz//tI5pLozFYtFHH32k9evX6z//+Y9Wr16t4cOHa86cOVq/fr3c3d2vup2KeD8tFkuhNyvmX72/1rZLoqirTYX1qyq4Wn/zj/mlS5fKz8+vQL2SzmjRokULa7CJjIzUuXPn9Oijj6pTp07WkPj999/rvvvu0x133KHXXntNdevW1Q033KBFixYVOmVXRbzW1/o+X0uf6tSpo3/84x/6+OOPNX/+fP3nP//RmTNnrDd0StKyZcs0dOhQRUZGauLEiapTp44cHR0VGxtb4AZAyfbKbXEeeOAB/fTTT5o4caJat24td3d35eXlKSIiosQ3lF1NXl6e/vGPfxQ5K8dNN9101TYOHjyomJgYRUZG6rXXXlPTpk31+OOPa/Xq1VddF9cnAi+gS/NJfvPNNzpz5ozNlbGdO3dal18u/2rV5f78809Vr17d+rXfRx99pCFDhmjOnDnWOhcuXFBaWlqhfdi9e7fuvPNO6/OzZ8/q6NGjuueee8q8X/mK+0dkwIABioqK0nvvvafz58/rhhtuUP/+/a95mx999JHOnz9f4Ap7YTp06KAOHTpo+vTpWr58uQYNGqT3339fjzzySLn/ilVR793lN0x5eXkV+tXxlVfnStO3Bg0aKC8vT7t377a5OSw1NVVpaWmlmpv4atspzbFcUtf6PuQPGahTp441sJaHGTNm6JNPPtH06dO1YMECSdLHH38sFxcXrV69Ws7Ozta6ixYtKtM2fHx85OrqWuixc+Vcz5X1Pl/NoEGDlJCQoK+++krLly+Xh4eHevbsaV3+0UcfqVGjRlq5cqXNexsTE1PmbZ4+fVqJiYmaOnWqzbRohb1uly+7/Orxnj17lJeXV+wNjEFBQTp79uw1HUf5v5Y5d+5c1a1bV9OnT9fYsWP1/vvva8CAAWVuF1UXQxoASffcc49yc3MLXNl8+eWXZbFY1L17d5vy5ORkm/FoBw8e1Keffqpu3bpZr8w4OjoWuBrz6quvFnmV8I033rAZxxofH6+cnJwC2y4LNze3IoO2t7e3unfvrmXLlundd99VRESEvL29r2l7W7Zs0ZNPPikvL68CY/Qud/r06QKvUf7d4fnDGvJnXSiq/6W1atUqHT582Pp848aN2rBhg83rHBQUpJ07d9pMq7Vlyxb9+OOPNm2Vpm/5f7hceQf5Sy+9JEkFZg4oq9IeyyVV3DFUEuHh4fLw8NC///3vQsdrl/WX+YKCgtS3b18tXrzY+uMTjo6OslgsNp+1ffv2lfnHVxwdHRUeHq5Vq1bpwIED1vIdO3YUuCJYWe/z1URGRqp69ep67bXX9NVXX6lPnz42c+bmn6cu//xt2LChzFMRFtWmVPC1uNz8+fNtnr/66quSVOxx+sADDyg5ObnQq7FpaWnKyckptp+ffPKJPvvsM/3rX/+yfiswevRohYSEKCoqShkZGcWuj+sTV3gBST179tSdd96pZ599Vvv27VOrVq20Zs0affrpp3ryySdtbmiRpObNmys8PNxmWjLp0nys+e69914tXbpUnp6eatasmZKTk/XNN9/YTJF2uezsbN19993WqYdee+01derUSffdd981719ISIi++eYbvfTSS/L391fDhg2tN8FIl4Y15E/mP23atFK1/f333+vChQvKzc3VyZMn9eOPP+qzzz6Tp6enPvnkk0K/vs63ZMkSvfbaa+rdu7eCgoJ05swZvfnmm/Lw8LAGB1dXVzVr1kwrVqzQTTfdpFq1aql58+bFDpUoTnBwsDp16qRRo0YpKytLcXFxql27ts3Xo8OHD9dLL72k8PBwjRgxQseOHdOCBQt0yy232PxjWJq+tWrVSkOGDNEbb7yhtLQ0denSRRs3btSSJUsUGRlpc3X/WpT2WC6pkJAQxcfH64UXXlBwcLDq1KlT6M+zFsXDw0Px8fF6+OGH1aZNGw0YMEA+Pj46cOCAvvjiC91+++1lHkozceJEffDBB4qLi9OMGTPUo0cPvfTSS4qIiNCDDz6oY8eOaf78+QoODi7zT+pOnTpVCQkJ6ty5s0aPHq2cnBy9+uqruuWWW2zarKz3+Wrc3d0VGRlpHcJx+XAG6dL5aeXKlerdu7d69OihvXv3asGCBWrWrJnOnj1bpm16eHjojjvu0KxZs3Tx4kXVq1dPa9assc6DXpi9e/fqvvvuU0REhJKTk7Vs2TI9+OCDatWqVZHrTJw4UZ999pnuvfde61R9mZmZ+v333/XRRx9p3759Rf7RfubMGY0bN0633nqrzY2dDg4OWrBggUJDQ/Xss89agzdMxE6zQwDlKn9qpOKmtzKMS9NKubm5FbrszJkzxlNPPWX4+/sbN9xwg9G4cWPjxRdftJlqyTAuTWP0+OOPG8uWLTMaN25sODs7G7feemuB6YJOnz5tDBs2zPD29jbc3d2N8PBwY+fOnQWm2Mnv+7p164yRI0caXl5ehru7uzFo0CDj5MmTNm2WdVqynTt3GnfccYfh6upqSCowRVlWVpbh5eVleHp6GufPny/2NcyXP01U/uOGG24wfHx8jDvuuMOYPn16gSmMLt/X/GnJNm3aZAwcONCoX7++4ezsbNSpU8e49957baZ8MwzD+Omnn4yQkBDDycnJZhqw4t7PoqYle/HFF405c+YYAQEBhrOzs9G5c2ebKZDyLVu2zGjUqJHh5ORktG7d2li9enWBNovrW2Hvw8WLF42pU6caDRs2NG644QYjICDAiI6ONi5cuGBTr0GDBkaPHj0K9Kmo6dKuVNJjuTTTkqWkpBg9evQwatSoYUiy9qOoz17+8XHl52Lt2rVGeHi44enpabi4uBhBQUHG0KFDC7znV7raNHhdu3Y1PDw8rNOgvf3229bPZ9OmTY1FixYV+p7kf56vdOXn1DAMY926ddb3ulGjRsaCBQsq5H0urE+XH78l9cUXXxiSjLp169pMUWYYhpGXl2f8+9//Nho0aGA9h33++efFfm6uVNj559ChQ0bv3r2NmjVrGp6ensb9999vHDlypMD0ffmv2/bt241+/foZNWrUMLy8vIwxY8YUOAcV9l6cOXPGiI6ONoKDgw0nJyfD29vbuO2224zZs2fbTO94pSeeeMJwcHAoMI1dvjFjxhgODg5XPR5x/bEYRhW9AwJApcnJyZG/v7969uypt99+297dAQCgXDGGF4BWrVql48ePa/DgwfbuCgAA5Y4rvMDf2IYNG7R161ZNmzZN3t7ehU4MDwDA9Y4rvMDfWHx8vEaNGqU6deoU+9v1AABcz6pE4J0/f74CAwPl4uKi0NBQbdy4sci6K1euVNu2bVWzZk25ubmpdevWWrp0qU2doUOHymKx2DwiIiIqejeA687ixYuVk5OjX375pcyzHgAAUNXZfVqyFStWKCoqyjodSFxcnMLDw7Vr1y7VqVOnQP1atWrp2WefVdOmTeXk5KTPP/9cw4YNU506dWwmuI+IiLCZZPzyyccBAADw92H3MbyhoaFq166ddf7FvLw8BQQEaOzYsZo0aVKJ2mjTpo169OhhnT906NChSktLK/Mk4wAAADAPu17hzc7O1q+//qro6GhrmYODg8LCwkr0ay+GYejbb7/Vrl27NHPmTJtlSUlJqlOnjry8vHTXXXfphRdeKHLC/6ysLOuvOkmXQvepU6dUu3btcv9ZUwAAAFw7wzB05swZ+fv7y8Gh+FG6dg28J06cUG5urnx9fW3KfX19rb/7Xpj09HTVq1dPWVlZcnR01GuvvaZ//OMf1uURERHq06ePGjZsqL/++kvPPPOMunfvruTkZOtPH14uNjbW5heyAAAAcH04ePCgbrzxxmLr2H0Mb1nUqFFDmzdv1tmzZ5WYmKioqCg1atRIXbt2lSQNGDDAWrdFixZq2bKlgoKClJSUpLvvvrtAe9HR0YqKirI+T09PV/369XXw4EF5eHhU+P4AAACgdDIyMhQQEKAaNWpcta5dA6+3t7ccHR2VmppqU56amio/P78i13NwcFBwcLAkqXXr1tqxY4diY2OtgfdKjRo1kre3t/bs2VNo4HV2di70pjYPDw8CLwAAQBVWkuGndp2WzMnJSSEhIUpMTLSW5eXlKTExUR07dixxO3l5eTZjcK906NAhnTx5UnXr1r2m/gIAAOD6Y/chDVFRURoyZIjatm2r9u3bKy4uTpmZmRo2bJgkafDgwapXr55iY2MlXRpv27ZtWwUFBSkrK0tffvmlli5dqvj4eEnS2bNnNXXqVPXt21d+fn7666+/9PTTTys4ONhm2jIAAAD8Pdg98Pbv31/Hjx/X5MmTlZKSotatWyshIcF6I9uBAwds7rzLzMzU6NGjdejQIbm6uqpp06ZatmyZ+vfvL0lydHTU1q1btWTJEqWlpcnf31/dunXTtGnTmIsXAADgb8ju8/BWRRkZGfL09FR6ejpjeAEAAKqg0uS1KvHTwgAAAEBFIfACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMLVq9u4ALrFMtdi7C6ggRoxhnw1bOKZMybDT8QQA1zGu8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFMj8AIAAMDUCLwAAAAwNQIvAAAATI3ACwAAAFOrEoF3/vz5CgwMlIuLi0JDQ7Vx48Yi665cuVJt27ZVzZo15ebmptatW2vp0qU2dQzD0OTJk1W3bl25uroqLCxMu3fvrujdAAAAQBVk98C7YsUKRUVFKSYmRps2bVKrVq0UHh6uY8eOFVq/Vq1aevbZZ5WcnKytW7dq2LBhGjZsmFavXm2tM2vWLM2dO1cLFizQhg0b5ObmpvDwcF24cKGydgsAAABVhMUwDMOeHQgNDVW7du00b948SVJeXp4CAgI0duxYTZo0qURttGnTRj169NC0adNkGIb8/f01fvx4TZgwQZKUnp4uX19fLV68WAMGDLhqexkZGfL09FR6ero8PDzKvnOlYJlqqZTtoPIZMXb6iFk4pkzJvqdsAKgySpPX7HqFNzs7W7/++qvCwsKsZQ4ODgoLC1NycvJV1zcMQ4mJidq1a5fuuOMOSdLevXuVkpJi06anp6dCQ0OLbDMrK0sZGRk2DwAAAJiDXQPviRMnlJubK19fX5tyX19fpaSkFLleenq63N3d5eTkpB49eujVV1/VP/7xD0myrleaNmNjY+Xp6Wl9BAQEXMtuAQAAoAqx+xjesqhRo4Y2b96sn3/+WdOnT1dUVJSSkpLK3F50dLTS09Otj4MHD5ZfZwEAAGBX1ey5cW9vbzk6Oio1NdWmPDU1VX5+fkWu5+DgoODgYElS69attWPHDsXGxqpr167W9VJTU1W3bl2bNlu3bl1oe87OznJ2dr7GvQEAAEBVZNcrvE5OTgoJCVFiYqK1LC8vT4mJierYsWOJ28nLy1NWVpYkqWHDhvLz87NpMyMjQxs2bChVmwAAADAHu17hlaSoqCgNGTJEbdu2Vfv27RUXF6fMzEwNGzZMkjR48GDVq1dPsbGxki6Nt23btq2CgoKUlZWlL7/8UkuXLlV8fLwkyWKx6Mknn9QLL7ygxo0bq2HDhnr++efl7++vyMhIe+0mAAAA7MTugbd///46fvy4Jk+erJSUFLVu3VoJCQnWm84OHDggB4f/XYjOzMzU6NGjdejQIbm6uqpp06ZatmyZ+vfvb63z9NNPKzMzUyNHjlRaWpo6deqkhIQEubi4VPr+AQAAwL7sPg9vVcQ8vChPzMOLcsUpGwAkXUfz8AIAAAAVjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADC1KhF458+fr8DAQLm4uCg0NFQbN24ssu6bb76pzp07y8vLS15eXgoLCytQf+jQobJYLDaPiIiIit4NAAAAVEF2D7wrVqxQVFSUYmJitGnTJrVq1Urh4eE6duxYofWTkpI0cOBArV27VsnJyQoICFC3bt10+PBhm3oRERE6evSo9fHee+9Vxu4AAACgirEYhmHYswOhoaFq166d5s2bJ0nKy8tTQECAxo4dq0mTJl11/dzcXHl5eWnevHkaPHiwpEtXeNPS0rRq1aoy9SkjI0Oenp5KT0+Xh4dHmdooLctUS6VsB5XPiLHTR8zCMWVK9j1lA0CVUZq8ZtcrvNnZ2fr1118VFhZmLXNwcFBYWJiSk5NL1Ma5c+d08eJF1apVy6Y8KSlJderUUZMmTTRq1CidPHmyyDaysrKUkZFh8wAAAIA52DXwnjhxQrm5ufL19bUp9/X1VUpKSona+L//+z/5+/vbhOaIiAi98847SkxM1MyZM7Vu3Tp1795dubm5hbYRGxsrT09P6yMgIKDsOwUAAIAqpZq9O3AtZsyYoffff19JSUlycXGxlg8YMMD6/y1atFDLli0VFBSkpKQk3X333QXaiY6OVlRUlPV5RkYGoRcAAMAk7HqF19vbW46OjkpNTbUpT01NlZ+fX7Hrzp49WzNmzNCaNWvUsmXLYus2atRI3t7e2rNnT6HLnZ2d5eHhYfMAAACAOdg18Do5OSkkJESJiYnWsry8PCUmJqpjx45Frjdr1ixNmzZNCQkJatu27VW3c+jQIZ08eVJ169Ytl34DAADg+mH3acmioqL05ptvasmSJdqxY4dGjRqlzMxMDRs2TJI0ePBgRUdHW+vPnDlTzz//vBYuXKjAwEClpKQoJSVFZ8+elSSdPXtWEydO1Pr167Vv3z4lJiaqV69eCg4OVnh4uF32EQAAAPZj9zG8/fv31/HjxzV58mSlpKSodevWSkhIsN7IduDAATk4/C+Xx8fHKzs7W/369bNpJyYmRlOmTJGjo6O2bt2qJUuWKC0tTf7+/urWrZumTZsmZ2fnSt03AAAA2J/d5+GtipiHF+WJeXhRrjhlA4Ck62geXgAAAKCiEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgamUKvGvXri3vfgAAAAAVokyBNyIiQkFBQXrhhRd08ODB8u4TAAAAUG7KFHgPHz6sMWPG6KOPPlKjRo0UHh6uDz74QNnZ2WXqxPz58xUYGCgXFxeFhoZq48aNRdZ988031blzZ3l5ecnLy0thYWEF6huGocmTJ6tu3bpydXVVWFiYdu/eXaa+AQAA4PpWpsDr7e2tp556Sps3b9aGDRt00003afTo0fL399e4ceO0ZcuWEre1YsUKRUVFKSYmRps2bVKrVq0UHh6uY8eOFVo/KSlJAwcO1Nq1a5WcnKyAgAB169ZNhw8fttaZNWuW5s6dqwULFmjDhg1yc3NTeHi4Lly4UJbdBQAAwHXMYhiGca2NHDlyRG+88YZmzJihatWq6cKFC+rYsaMWLFigW265pdh1Q0ND1a5dO82bN0+SlJeXp4CAAI0dO1aTJk266rZzc3Pl5eWlefPmafDgwTIMQ/7+/ho/frwmTJggSUpPT5evr68WL16sAQMGXLXNjIwMeXp6Kj09XR4eHiV4Ba6dZaqlUraDymfEXPNHrGwsHFOmdO2nbAAwhdLktTLP0nDx4kV99NFHuueee9SgQQOtXr1a8+bNU2pqqvbs2aMGDRro/vvvL7aN7Oxs/frrrwoLC/tfhxwcFBYWpuTk5BL149y5c7p48aJq1aolSdq7d69SUlJs2vT09FRoaGiRbWZlZSkjI8PmAQAAAHOoVpaVxo4dq/fee0+GYejhhx/WrFmz1Lx5c+tyNzc3zZ49W/7+/sW2c+LECeXm5srX19em3NfXVzt37ixRX/7v//5P/v7+1oCbkpJibePKNvOXXSk2NlZTp04t0fYAAABwfSlT4N2+fbteffVV9enTR87OzoXW8fb2rvDpy2bMmKH3339fSUlJcnFxKXM70dHRioqKsj7PyMhQQEBAeXQRAAAAdlamIQ0xMTG6//77C4TdnJwcfffdd5KkatWqqUuXLsW24+3tLUdHR6WmptqUp6amys/Pr9h1Z8+erRkzZmjNmjVq2bKltTx/vdK06ezsLA8PD5sHAAAAzKFMgffOO+/UqVOnCpSnp6frzjvvLHE7Tk5OCgkJUWJiorUsLy9PiYmJ6tixY5HrzZo1S9OmTVNCQoLatm1rs6xhw4by8/OzaTMjI0MbNmwotk0AAACYU5mGNBiGIUshd4CfPHlSbm5upWorKipKQ4YMUdu2bdW+fXvFxcUpMzNTw4YNkyQNHjxY9erVU2xsrCRp5syZmjx5spYvX67AwEDruFx3d3e5u7vLYrHoySef1AsvvKDGjRurYcOGev755+Xv76/IyMiy7C4AAACuY6UKvH369JEkWSwWDR061GZIQ25urrZu3arbbrutVB3o37+/jh8/rsmTJyslJUWtW7dWQkKC9aazAwcOyMHhfxei4+PjlZ2drX79+tm0ExMToylTpkiSnn76aWVmZmrkyJFKS0tTp06dlJCQcE3jfAEAAHB9KtU8vPlXXZcsWaIHHnhArq6u1mVOTk4KDAzUo48+Km9v7/LvaSViHl6UJ+bhRbliHl4AkFS6vFaqK7yLFi2SJAUGBmrChAmlHr4AAAAAVLYyjeGNiYkp734AAAAAFaLEgbdNmzZKTEyUl5eXbr311kJvWsu3adOmcukcAAAAcK1KHHh79eplvUmN2Q4AAABwvSjVTWt/F9y0hvLETWsoV5yyAUBS6fJamX54AgAAALhelHhIg5eXV7Hjdi9X2K+wAQAAAPZQ4sAbFxdXgd0AAAAAKkaJA++QIUMqsh8AAABAhShx4M3IyLAOCM7IyCi2bmXd6AUAAABcTanG8B49elR16tRRzZo1Cx3PaxiGLBaLcnNzy7WTAAAAQFmVOPB+++23qlWrliRp7dq1FdYhAAAAoDyVOPB26dKl0P8HAAAAqrISB94rnT59Wm+//bZ27NghSWrWrJmGDRtmvQoMAAAAVAVl+uGJ7777ToGBgZo7d65Onz6t06dPa+7cuWrYsKG+++678u4jAAAAUGZlusL7+OOPq3///oqPj5ejo6MkKTc3V6NHj9bjjz+u33//vVw7CQAAAJRVma7w7tmzR+PHj7eGXUlydHRUVFSU9uzZU26dAwAAAK5VmQJvmzZtrGN3L7djxw61atXqmjsFAAAAlJcSD2nYunWr9f/HjRunJ554Qnv27FGHDh0kSevXr9f8+fM1Y8aM8u8lAAAAUEYWwzCMklR0cHCQxWLR1aqb4YcnMjIy5OnpqfT09Er71TjL1II/5AFzMGJK9BErf4X8OAxMoGSnbAAwvdLktRJf4d27d+81dwwAAACobCUOvA0aNKjIfgAAAAAVosw/PCFJ27dv14EDB5SdnW1Tft99911TpwAAAIDyUqbA+9///le9e/fW77//bjOu1/L/xwxe72N4AQAAYB5lmpbsiSeeUMOGDXXs2DFVr15d27Zt03fffae2bdsqKSmpnLsIAAAAlF2ZrvAmJyfr22+/lbe3txwcHOTg4KBOnTopNjZW48aN02+//Vbe/QQAAADKpExXeHNzc1WjRg1Jkre3t44cOSLp0o1tu3btKr/eAQAAANeoTFd4mzdvri1btqhhw4YKDQ3VrFmz5OTkpDfeeEONGjUq7z4CAAAAZVamwPvcc88pMzNTkvSvf/1L9957rzp37qzatWtrxYoV5dpBAAAA4FqUKfCGh4db/z84OFg7d+7UqVOn5OXlZZ2pAQBgHpzazcseP9431TK18jeKShFjxNi7C4W6pnl4JengwYOSpICAgGvuDAAAAFDeynTTWk5Ojp5//nl5enoqMDBQgYGB8vT01HPPPaeLFy+Wdx8BAACAMivTFd6xY8dq5cqVmjVrljp27Cjp0lRlU6ZM0cmTJxUfH1+unQQAAADKqkyBd/ny5Xr//ffVvXt3a1nLli0VEBCggQMHEngBAABQZZRpSIOzs7MCAwMLlDds2FBOTk7X2icAAACg3JQp8I4ZM0bTpk1TVlaWtSwrK0vTp0/XmDFjyq1zAAAAwLUq8ZCGPn362Dz/5ptvdOONN6pVq1aSpC1btig7O1t33313+fYQAAAAuAYlDryenp42z/v27WvznGnJAAAAUBWVOPAuWrSoIvsBAAAAVIhr+uGJ48ePa9euXZKkJk2ayMfHp1w6BQAAAJSXMt20lpmZqeHDh6tu3bq64447dMcdd8jf318jRozQuXPnyruPAAAAQJmVKfBGRUVp3bp1+s9//qO0tDSlpaXp008/1bp16zR+/Pjy7iMAAABQZmUa0vDxxx/ro48+UteuXa1l99xzj1xdXfXAAw/wwxMAAACoMsp0hffcuXPy9fUtUF6nTh2GNAAAAKBKKVPg7dixo2JiYnThwgVr2fnz5zV16lR17NixVG3Nnz9fgYGBcnFxUWhoqDZu3Fhk3W3btqlv374KDAyUxWJRXFxcgTpTpkyRxWKxeTRt2rRUfQIAAIB5lGlIQ1xcnCIiIgr88ISLi4tWr15d4nZWrFihqKgoLViwQKGhoYqLi1N4eLh27dqlOnXqFKh/7tw5NWrUSPfff7+eeuqpItu95ZZb9M0331ifV6t2TZNRAAAA4DpWpiTYokUL7d69W++++6527twpSRo4cKAGDRokV1fXErfz0ksv6dFHH9WwYcMkSQsWLNAXX3yhhQsXatKkSQXqt2vXTu3atZOkQpfnq1atmvz8/EqzSwAAADCpUgfeixcvqmnTpvr888/16KOPlnnD2dnZ+vXXXxUdHW0tc3BwUFhYmJKTk8vcriTt3r1b/v7+cnFxUceOHRUbG6v69esXWT8rK0tZWVnW5xkZGde0fQAAAFQdpR7De8MNN9iM3S2rEydOKDc3t8DNb76+vkpJSSlzu6GhoVq8eLESEhIUHx+vvXv3qnPnzjpz5kyR68TGxsrT09P64GeSAQAAzKNMN609/vjjmjlzpnJycsq7P9ese/fuuv/++9WyZUuFh4fryy+/VFpamj744IMi14mOjlZ6err1cfDgwUrsMQAAACpSmcbw/vzzz0pMTNSaNWvUokULubm52SxfuXLlVdvw9vaWo6OjUlNTbcpTU1PLdfxtzZo1ddNNN2nPnj1F1nF2dpazs3O5bRMAAABVR5mu8NasWVN9+/ZVeHi4/P39bYYDeHp6lqgNJycnhYSEKDEx0VqWl5enxMTEUk9tVpyzZ8/qr7/+Ut26dcutTQAAAFw/SnWFNy8vTy+++KL+/PNPZWdn66677tKUKVNKNTPD5aKiojRkyBC1bdtW7du3V1xcnDIzM62zNgwePFj16tVTbGyspEs3um3fvt36/4cPH9bmzZvl7u6u4OBgSdKECRPUs2dPNWjQQEeOHFFMTIwcHR01cODAMvURAAAA17dSBd7p06drypQpCgsLk6urq+bOnavjx49r4cKFZdp4//79dfz4cU2ePFkpKSlq3bq1EhISrDeyHThwQA4O/7sIfeTIEd16663W57Nnz9bs2bPVpUsXJSUlSZIOHTqkgQMH6uTJk/Lx8VGnTp20fv16+fj4lKmPAAAAuL5ZDMMwSlq5cePGmjBhgh577DFJ0jfffKMePXro/PnzNsH0epeRkSFPT0+lp6fLw8OjUrZpmWqplO2g8hkxJf6IlS8Lx5QplfyUXa44nMzLHofUVMvUyt8oKkWMEVNp2ypNXitVSj1w4IDuuece6/OwsDBZLBYdOXKkbD0FAAAAKlipAm9OTo5cXFxsym644QZdvHixXDsFAAAAlJdSjeE1DENDhw61mcLrwoUL+uc//2kzNVlJpiUDAAAAKkOpAu+QIUMKlD300EPl1hkAAACgvJUq8C5atKii+gEAAABUCPNMrQAAAAAUgsALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNQIvAAAADA1Ai8AAABMjcALAAAAUyPwAgAAwNTsHnjnz5+vwMBAubi4KDQ0VBs3biyy7rZt29S3b18FBgbKYrEoLi7umtsEAACAudk18K5YsUJRUVGKiYnRpk2b1KpVK4WHh+vYsWOF1j937pwaNWqkGTNmyM/Pr1zaBAAAgLnZNfC+9NJLevTRRzVs2DA1a9ZMCxYsUPXq1bVw4cJC67dr104vvviiBgwYIGdn53JpEwAAAOZmt8CbnZ2tX3/9VWFhYf/rjIODwsLClJycXKltZmVlKSMjw+YBAAAAc7Bb4D1x4oRyc3Pl6+trU+7r66uUlJRKbTM2Nlaenp7WR0BAQJm2DwAAgKrH7jetVQXR0dFKT0+3Pg4ePGjvLgEAAKCcVLPXhr29veXo6KjU1FSb8tTU1CJvSKuoNp2dnYscEwwAAIDrm92u8Do5OSkkJESJiYnWsry8PCUmJqpjx45Vpk0AAABc3+x2hVeSoqKiNGTIELVt21bt27dXXFycMjMzNWzYMEnS4MGDVa9ePcXGxkq6dFPa9u3brf9/+PBhbd68We7u7goODi5RmwAAAPh7sWvg7d+/v44fP67JkycrJSVFrVu3VkJCgvWmswMHDsjB4X8XoY8cOaJbb73V+nz27NmaPXu2unTpoqSkpBK1CQAAgL8Xi2EYhr07UdVkZGTI09NT6enp8vDwqJRtWqZaKmU7qHxGjJ0+YhaOKVOy0ymbw8m87HFITbVMrfyNolLEGDGVtq3S5DVmaQAAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZWJQLv/PnzFRgYKBcXF4WGhmrjxo3F1v/www/VtGlTubi4qEWLFvryyy9tlg8dOlQWi8XmERERUZG7AAAAgCrK7oF3xYoVioqKUkxMjDZt2qRWrVopPDxcx44dK7T+Tz/9pIEDB2rEiBH67bffFBkZqcjISP3xxx829SIiInT06FHr47333quM3QEAAEAVY/fA+9JLL+nRRx/VsGHD1KxZMy1YsEDVq1fXwoULC63/yiuvKCIiQhMnTtTNN9+sadOmqU2bNpo3b55NPWdnZ/n5+VkfXl5elbE7AAAAqGLsGnizs7P166+/KiwszFrm4OCgsLAwJScnF7pOcnKyTX1JCg8PL1A/KSlJderUUZMmTTRq1CidPHmyyH5kZWUpIyPD5gEAAABzsGvgPXHihHJzc+Xr62tT7uvrq5SUlELXSUlJuWr9iIgIvfPOO0pMTNTMmTO1bt06de/eXbm5uYW2GRsbK09PT+sjICDgGvcMAAAAVUU1e3egIgwYMMD6/y1atFDLli0VFBSkpKQk3X333QXqR0dHKyoqyvo8IyOD0AsAAGASdr3C6+3tLUdHR6WmptqUp6amys/Pr9B1/Pz8SlVfkho1aiRvb2/t2bOn0OXOzs7y8PCweQAAAMAc7Bp4nZycFBISosTERGtZXl6eEhMT1bFjx0LX6dixo019Sfr666+LrC9Jhw4d0smTJ1W3bt3y6TgAAACuG3afpSEqKkpvvvmmlixZoh07dmjUqFHKzMzUsGHDJEmDBw9WdHS0tf4TTzyhhIQEzZkzRzt37tSUKVP0yy+/aMyYMZKks2fPauLEiVq/fr327dunxMRE9erVS8HBwQoPD7fLPgIAAMB+7D6Gt3///jp+/LgmT56slJQUtW7dWgkJCdYb0w4cOCAHh//l8ttuu03Lly/Xc889p2eeeUaNGzfWqlWr1Lx5c0mSo6Ojtm7dqiVLligtLU3+/v7q1q2bpk2bJmdnZ7vsIwAAAOzHYhiGYe9OVDUZGRny9PRUenp6pY3ntUy1VMp2UPmMGDt9xCwcU6Zkp1M2h5N52eOQmmqZWvkbRaWIMWIqbVulyWt2H9IAAAAAVCQCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1Ai8AAAAMDUCLwAAAEyNwAsAAABTI/ACAADA1KpE4J0/f74CAwPl4uKi0NBQbdy4sdj6H374oZo2bSoXFxe1aNFCX375pc1ywzA0efJk1a1bV66urgoLC9Pu3bsrchcAAABQRdk98K5YsUJRUVGKiYnRpk2b1KpVK4WHh+vYsWOF1v/pp580cOBAjRgxQr/99psiIyMVGRmpP/74w1pn1qxZmjt3rhYsWKANGzbIzc1N4eHhunDhQmXtFgAAAKoIi2EYhj07EBoaqnbt2mnevHmSpLy8PAUEBGjs2LGaNGlSgfr9+/dXZmamPv/8c2tZhw4d1Lp1ay1YsECGYcjf31/jx4/XhAkTJEnp6eny9fXV4sWLNWDAgKv2KSMjQ56enkpPT5eHh0c57WnxLFMtlbIdVD4jxk4fMQvHlCnZ6ZTN4WRe9jikplqmVv5GUSlijJhK21Zp8lq1SupTobKzs/Xrr78qOjraWubg4KCwsDAlJycXuk5ycrKioqJsysLDw7Vq1SpJ0t69e5WSkqKwsDDrck9PT4WGhio5ObnQwJuVlaWsrCzr8/T0dEmXXshKw8Vn06rU4wjmx/GEcmaPQ+oC/+iZVmX+m5e/rZJcu7Vr4D1x4oRyc3Pl6+trU+7r66udO3cWuk5KSkqh9VNSUqzL88uKqnOl2NhYTZ1a8K/NgICAku0IUAzPGZ727gLMxJPjCeWLQwrlaYbnjErf5pkzZ+R5lQPZroG3qoiOjra5apyXl6dTp06pdu3asvA9XrnLyMhQQECADh48WGlDRmBeHE8oTxxPKG8cUxXHMAydOXNG/v7+V61r18Dr7e0tR0dHpaam2pSnpqbKz8+v0HX8/PyKrZ//39TUVNWtW9emTuvWrQtt09nZWc7OzjZlNWvWLM2uoAw8PDz48KPccDyhPHE8obxxTFWMq13ZzWfXWRqcnJwUEhKixMREa1leXp4SExPVsWPHQtfp2LGjTX1J+vrrr631GzZsKD8/P5s6GRkZ2rBhQ5FtAgAAwLzsPqQhKipKQ4YMUdu2bdW+fXvFxcUpMzNTw4YNkyQNHjxY9erVU2xsrCTpiSeeUJcuXTRnzhz16NFD77//vn755Re98cYbkiSLxaInn3xSL7zwgho3bqyGDRvq+eefl7+/vyIjI+21mwAAALATuwfe/v376/jx45o8ebJSUlLUunVrJSQkWG86O3DggBwc/nch+rbbbtPy5cv13HPP6ZlnnlHjxo21atUqNW/e3Frn6aefVmZmpkaOHKm0tDR16tRJCQkJcnFxqfT9Q0HOzs6KiYkpMIwEKAuOJ5QnjieUN46pqsHu8/ACAAAAFcnuv7QGAAAAVCQCLwAAAEyNwAsAAABTI/Ci0i1evFhJSUn27gauY/v27dOUKVPs3Q2YFOcoXCvOUVUPgRdVxsmTJxURESF/f385OzsrICBAY8aMqdTf5cb17dSpUxo7dqyaNGkiV1dX1a9fX+PGjVN6erq9uwaTGDdunEJCQuTs7FzkjxkBJWEYhrp37y6LxaJVq1bZuzumR+BFueratasWL15c6LK1a9fq9ttv1xNPPKHevXurTZs2io+Pty53cHBQr1699Nlnn+nPP//U4sWL9c033+if//xnJfUeVd3evXvVu3dvdejQQbNmzVLTpk1tjo8jR47oyJEjmj17tv744w8tXrxYCQkJGjFihB17jarkWs5R+YYPH67+/ftXcE9xPbraOepycXFxslgsldzDvy+7z8OLv4e0tDT16tVLAwYMUEREhOrWrStPT0+dOHHCWsfLy0ujRo2yPm/QoIFGjx6tF1980R5dRhU0ePBg5ebmKj4+Xl9//bV69eql7777zrq8efPm+vjjj63Pg4KCNH36dD300EPKyclRtWqc8lC4kpyjJGnu3LmSpOPHj2vr1q326CqqsKudo/Jt3rxZc+bM0S+//KK6devaoad/P5z9USn27NmjM2fOKCYmRl9//bUCAwPVtWvXYtc5cuSIVq5cqS5dulROJ1Hl/fbbb3r99dd16623asuWLQoPD1d4eHix66Snp8vDw4Owi2KV5RwFXKkk56hz587pwQcf1Pz58+Xn52ennv79MKQBlaJJkyby9vbWpEmTtHv37mLrDhw4UNWrV1e9evXk4eGht956q5J6iaru9ttvV1xcnL7//vsS1T9x4oSmTZumkSNHVnDPcL0rzTkKKEpJzlFPPfWUbrvtNvXq1asSewYZwDWYPn264ebmZn04ODgYzs7ONmX79+83DMMwtm7davTp08fw9PQ03N3djZ49exqbNm0q0ObRo0eNHTt2GJ9++qnRrFkzY9SoUZW9W6gCli1bZnMcfffdd8bx48eNMWPGGDfeeKNRrVo1o0OHDsaHH35Y6Prp6elG+/btjYiICCM7O7uSe4+qoiLOUYZhGDExMUarVq0qcU9Q1ZTlHPXpp58awcHBxpkzZ6xlkoxPPvnEDnvw98JPC+OanDp1SqdOnbI+HzRokPr27as+ffpYywIDA22+Tl68eLHOnTun5ORk/ec//9Hu3bvl4+NTaPs//PCDOnfurCNHjjDO6W/mzJkzSk1NtT6vV6+eXF1dJV2a8mfGjBkKDAzUs88+q6+++krdunWzWTc8PFzVq1fX559/LhcXl0rvP6qGijpHTZkyRatWrdLmzZsrfB9QNZXlHPXkk09q7ty5cnD43xfsubm5cnBwUOfOnZkOrwIxqA3XpFatWqpVq5b1uaurq+rUqaPg4OBi12vWrJkefvhhLVu2TFu3btXdd99daL28vDxJUlZWVvl1GteFGjVqqEaNGkUu9/Pz06RJk/Thhx/q+++/twbejIwMhYeHy9nZWZ999hlh92+uos9R+Psqyzlq0qRJeuSRR2zqtWjRQi+//LJ69uxZ0V3+WyPwolJs2rRJn332mQYOHKicnBylpaXpxRdflIuLi5o1ayZJ+vLLL5Wamqp27drJ3d1d27Zt08SJE3X77bcrMDDQvjuAKmHEiBF67LHH5ObmpqysLK1cuVLbtm3T888/L+lS2O3WrZvOnTunZcuWKSMjwzqPs4+PjxwdHe3ZfVRhJTlHSZdubjt79qxSUlJ0/vx56xXeZs2aycnJyU69R1VxtXOUn59foTeq1a9fXw0bNqzs7v6tEHhRKerWrauDBw8qIiJChw8flqOjo26++WZ9/PHH1qEKrq6uevPNN/XUU08pKytLAQEB6tOnjyZNmmTn3qOqqFOnjoYPH669e/cqKytL9evX17Rp0xQZGSnpUmjZsGGDJBW4grd3717+cEKRSnKOkqRHHnlE69atsz6/9dZbJXF84ZKrnaNgP4zhRaVbvHgxU/7gmuzbt0+LFy/mpztRIThH4Vpxjqp6mJYMAAAApsYVXgAAAJgaV3gBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwCqqK5du+rJJ5+0dzeuasqUKfL19ZXFYtGqVavs3R0AKIDACwDlrGfPnoqIiCh02ffffy+LxaKtW7dWcq8qxo4dOzR16lS9/vrrOnr0qLp3716gzpdffiknJydt2rTJpnzOnDny9vZWSkpKZXUXwN8UgRcAytmIESP09ddf69ChQwWWLVq0SG3btlXLli3t0LPy99dff0mSevXqJT8/Pzk7Oxeoc88992jw4MEaPHiwsrKyJEnbt2/Xc889p/nz58vPz69S+wzg74fACwDl7N5775WPj48WL15sU3727Fl9+OGHGjFihE6ePKmBAweqXr16ql69ulq0aKH33nuv2HYLGzJQs2ZNm+0cPHhQDzzwgGrWrKlatWqpV69e2rdvn3V5UlKS2rdvLzc3N9WsWVO333679u/fX+Q2f//9d911111ydXVV7dq1NXLkSJ09e1bSpaEMPXv2lCQ5ODjIYrEU2c7LL7+ss2fPKiYmRjk5ORoyZIh69uyp/v37F7vPAFAeCLwAUM6qVaumwYMHa/Hixbr819s//PBD5ebmauDAgbpw4YJCQkL0xRdf6I8//tDIkSP18MMPa+PGjWXe7sWLFxUeHq4aNWro+++/148//ih3d3dFREQoOztbOTk5ioyMVJcuXbR161YlJydr5MiRRQbVzMxMhYeHy8vLSz///LM+/PBDffPNNxozZowkacKECVq0aJEk6ejRozp69GiRfatRo4YWLlyoOXPmaNCgQTp48KDi4+PLvK8AUBrV7N0BADCj4cOH68UXX9S6devUtWtXSZeGM/Tt21eenp7y9PTUhAkTrPXHjh2r1atX64MPPlD79u3LtM0VK1YoLy9Pb731ljXELlq0SDVr1lRSUpLatm2r9PR03XvvvQoKCpIk3XzzzUW2t3z5cl24cEHvvPOO3NzcJEnz5s1Tz549NXPmTPn6+qpmzZqSVKJhCXfddZf69eun999/XytWrFDt2rXLtJ8AUFpc4QWACtC0aVPddtttWrhwoSRpz549+v777zVixAhJUm5urqZNm6YWLVqoVq1acnd31+rVq3XgwIEyb3PLli3as2ePatSoIXd3d7m7u6tWrVq6cOGC/vrrL9WqVUtDhw5VeHi4evbsqVdeeaXYq7I7duxQq1atrGFXkm6//Xbl5eVp165dpe7f4cOHlZCQoOrVq+v7778v0z4CQFkQeAGggowYMUIff/yxzpw5o0WLFikoKEhdunSRJL344ot65ZVX9H//939au3atNm/erPDwcGVnZxfZnsVisRkiIV0axpDv7NmzCgkJ0ebNm20ef/75px588EFJl674Jicn67bbbtOKFSt00003af369RWw9wU9+uijCgkJ0eeff674+HitW7euUrYLAAReAKggDzzwgBwcHLR8+XK98847Gj58uHWowY8//qhevXrpoYceUqtWrdSoUSP9+eefxbbn4+Njc0V29+7dOnfunPV5mzZttHv3btWpU0fBwcE2D09PT2u9W2+9VdHR0frpp5/UvHlzLV++vNDt3XzzzdqyZYsyMzOtZT/++KMcHBzUpEmTUr0Wb731ln744Qe9/fbbuvPOOzVq1CgNHz7cpm0AqCgEXgCoIO7u7urfv7+io6N19OhRDR061LqscePG+vrrr/XTTz9px44deuyxx5Samlpse3fddZfmzZun3377Tb/88ov++c9/6oYbbrAuHzRokLy9vdWrVy99//332rt3r5KSkjRu3DgdOnRIe/fuVXR0tJKTk7V//36tWbNGu3fvLnIc76BBg+Ti4qIhQ4bojz/+0Nq1azV27Fg9/PDD8vX1LfHrsH//fkVFRWn27Nlq0KCBJGnmzJmyWCyaNGlSidsBgLIi8AJABRoxYoROnz6t8PBw+fv7W8ufe+45tWnTRuHh4eratav8/PwUGRlZbFtz5sxRQECAOnfurAcffFATJkxQ9erVrcurV6+u7777TvXr11efPn108803a8SIEbpw4YI8PDxUvXp17dy5U3379tVNN92kkSNH6vHHH9djjz1W6PaqV6+u1atX69SpU2rXrp369eunu+++W/PmzSvx/huGoREjRqhjx44aOXKkTduLFy9maAOASmExrhwQBgAAAJgIV3gBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKZG4AUAAICpEXgBAABgagReAAAAmBqBFwAAAKb2/wDRRPSRrBOLWwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "## Example 1\n", + "import matplotlib.pyplot as plt\n", + "X_values = [\"+$3\",\"-$2\",\"+$1\",\"-$4\"]\n", + "proba=[2/6,2/6,1/6,1/6]\n", + "# Plotting the probability distribution\n", + "plt.figure(figsize=(8, 5))\n", + "bars = plt.bar(X_values, proba, color=['green', 'red', 'blue', 'purple'])\n", + "\n", + "# Adding labels and title\n", + "plt.xlabel('Values of X')\n", + "plt.ylabel('Probability')\n", + "plt.title('Probability Distribution of the Random Variable X')\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.16666666666666663\n" + ] + } + ], + "source": [ + "expected_value = proba[0]*(3)+proba[1]*(-2)+proba[2]*(1)+proba[3]*(-4)\n", + "print(expected_value)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4009401576225924" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.random.rand(1)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-13.95\n" + ] + } + ], + "source": [ + "money = 0\n", + "for sim in range(10000):\n", + " random = np.random.rand(1)[0]\n", + " if random <= (2/6):\n", + " money=money+3\n", + " elif random <= (4/6):\n", + " money=money-2\n", + " elif random <= (5/6):\n", + " money = money+1\n", + " else:\n", + " money = money-4\n", + "print(money/100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Example 2:** Suppose that items coming off a production line are classified as defective (D) or nondefective (N). Suppose that three items are chosen at\n", + "random from a day's production and are classified according to this scheme. Let us suppose that with probability 0.1 an item is defective and hence with\n", + "probability 0.9 an item is nondefective.\n", + " \n", + "1. Find the Sample Space for this experiment.\n", + "2. Compute the probability distribution\n", + "3. Plot the distribution of this random variable.\n", + "\n", + "We have a profit of $2 for each nondefective item and a loss of -$3 for each defective item:\n", + "\n", + " - Compute the probability distribution of this new random variable.\n", + " - Compute the expected profit/loss.\n", + " - How much should we decrease the defective to have a positive profit ?\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[('D', 'D', 'D'), ('D', 'D', 'N'), ('D', 'N', 'D'), ('D', 'N', 'N'), ('N', 'D', 'D'), ('N', 'D', 'N'), ('N', 'N', 'D'), ('N', 'N', 'N')]\n" + ] + } + ], + "source": [ + "## Example 2\n", + "import itertools\n", + "# Elements\n", + "elements = ['D', 'N']\n", + "\n", + "# Using itertools.product to get all combinations of 3 elements\n", + "sample_space = list(itertools.product(elements, repeat=3))\n", + "print(sample_space)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.7290000000000001, 0.24300000000000002, 0.027000000000000007, 0.0010000000000000002]\n" + ] + } + ], + "source": [ + "# Values of the random variable X (number of defective items)\n", + "X_values = [0, 1, 2, 3]\n", + "\n", + "# Probabilities of each value of X\n", + "probabilities = [\n", + " 1*(0.9)**3, # P(X=0)\n", + " 3 * (0.9)**2 * 0.1, # P(X=1)\n", + " 3 * 0.9 * (0.1)**2, # P(X=2)\n", + " 1*(0.1)**3 # P(X=3)\n", + "]\n", + "print(probabilities)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.500000000000001\n" + ] + } + ], + "source": [ + "expected_value=probabilities[0]*(3*2)+probabilities[1]*(2*2-1*3)+probabilities[2]*(1*2-2*3)+probabilities[3]*(0*2-3*3)\n", + "print(expected_value)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting the probability distribution\n", + "plt.figure(figsize=(8, 5))\n", + "plt.bar(X_values, probabilities, color=['blue', 'green', 'red', 'purple'])\n", + "\n", + "# Adding labels and title\n", + "plt.xlabel('Number of Defective Items in a Selection of 3')\n", + "plt.ylabel('Probability')\n", + "plt.title('Probability Distribution of the Number of Defective Items')\n", + "\n", + "# Display the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Example 3:** Rockets are launched until the first successful launching has taken place. If this does not occur within 5 attempts, the experiment is halted and the equipment inspected.\n", + "Suppose that there is a constant probability of 0.8 of having a successful launching and that successive attempts are independent. Assume that the cost of the first launching\n", + "is $K=5$ dollars while subsequent launchings cost $K/ 3$ dollars. Whenever a successful launching takes place, a certain amount of information is obtained which may be expressed as financial gain of, say $C=15$ dollars. If $T$ is the net cost of this experiment, find\n", + "the probability distribution of $T$." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "## Example 3:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Example 4:**\n", + "The percentage of alcohol ($100X$) in a certain compound may be considered as a random variable, where X, $0 < X < 1$, has the following pdf:\n", + "$$\n", + "f(x) = 20\\times x^3\\times(1 - x), 0"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":4,"id":"98d5f012","metadata":{},"outputs":[],"source":["# TODO"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":2,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":3,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":4,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":5,"id":"98d5f012","metadata":{},"outputs":[{"ename":"TypeError","evalue":"_parse_args() got an unexpected keyword argument 'low'","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/israel/problems.ipynb Cell 7\u001b[0m line \u001b[0;36m4\n\u001b[1;32m 40\u001b[0m high \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m\n\u001b[1;32m 41\u001b[0m data \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marange(\u001b[39m-\u001b[39m\u001b[39m5\u001b[39m, \u001b[39m5\u001b[39m, \u001b[39m0.01\u001b[39m)\n\u001b[0;32m---> 43\u001b[0m pmf \u001b[39m=\u001b[39m duniform(data, low \u001b[39m=\u001b[39;49m low, high \u001b[39m=\u001b[39;49m high)\n\u001b[1;32m 44\u001b[0m cdf \u001b[39m=\u001b[39m puniform(data, low \u001b[39m=\u001b[39m low, high \u001b[39m=\u001b[39m high)\n\u001b[1;32m 45\u001b[0m ppf \u001b[39m=\u001b[39m quniform(data, low \u001b[39m=\u001b[39m low, high \u001b[39m=\u001b[39m high)\n","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/israel/problems.ipynb Cell 7\u001b[0m line \u001b[0;36m9\n\u001b[1;32m 5\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mduniform\u001b[39m(x, low \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m, high \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m):\n\u001b[1;32m 6\u001b[0m \u001b[39m \u001b[39m\u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m 7\u001b[0m \u001b[39m Calculates the point estimate of the uniform distribution\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[39m \"\"\"\u001b[39;00m\n\u001b[0;32m----> 9\u001b[0m result \u001b[39m=\u001b[39m uniform\u001b[39m.\u001b[39;49mpdf(x, low \u001b[39m=\u001b[39;49m \u001b[39m0\u001b[39;49m, scale \u001b[39m=\u001b[39;49m (high \u001b[39m-\u001b[39;49m low))\n\u001b[1;32m 11\u001b[0m \u001b[39mreturn\u001b[39;00m result\n","File \u001b[0;32m~/.local/lib/python3.11/site-packages/scipy/stats/_distn_infrastructure.py:1979\u001b[0m, in \u001b[0;36mrv_continuous.pdf\u001b[0;34m(self, x, *args, **kwds)\u001b[0m\n\u001b[1;32m 1958\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mpdf\u001b[39m(\u001b[39mself\u001b[39m, x, \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwds):\n\u001b[1;32m 1959\u001b[0m \u001b[39m \u001b[39m\u001b[39m\"\"\"Probability density function at x of the given RV.\u001b[39;00m\n\u001b[1;32m 1960\u001b[0m \n\u001b[1;32m 1961\u001b[0m \u001b[39m Parameters\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 1977\u001b[0m \n\u001b[1;32m 1978\u001b[0m \u001b[39m \"\"\"\u001b[39;00m\n\u001b[0;32m-> 1979\u001b[0m args, loc, scale \u001b[39m=\u001b[39m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_parse_args(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwds)\n\u001b[1;32m 1980\u001b[0m x, loc, scale \u001b[39m=\u001b[39m \u001b[39mmap\u001b[39m(asarray, (x, loc, scale))\n\u001b[1;32m 1981\u001b[0m args \u001b[39m=\u001b[39m \u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(asarray, args))\n","\u001b[0;31mTypeError\u001b[0m: _parse_args() got an unexpected keyword argument 'low'"]}],"source":["from scipy.stats import uniform\n","import matplotlib.pyplot as plt\n","\n","\n","def duniform(x, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the point estimate of the uniform distribution\n"," \"\"\"\n"," result = uniform.pdf(x, low = 0, scale = (high - low))\n","\n"," return result\n","\n","def puniform(q, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the cumulative of the uniform distribution\n"," \"\"\"\n"," result = uniform.cdf(q, low = 0, scale = (high - low))\n","\n"," return result\n","\n","def quniform(p, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the quantile function from the uniform distribution\n"," \"\"\"\n"," result = uniform.ppf(p, low = 0, scale = (high - low))\n","\n"," return result\n","\n","def runiform(n, low = 0, high = 1):\n"," \"\"\"\n"," Generates random variables from the uniform distribution\n"," \"\"\"\n"," result = uniform.rvs(n, low = 0, scale = (high - low))\n","\n"," return result\n","\n"]},{"cell_type":"code","execution_count":6,"id":"a2ea5ac2","metadata":{},"outputs":[{"ename":"TypeError","evalue":"_parse_args() got an unexpected keyword argument 'low'","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/israel/problems.ipynb Cell 8\u001b[0m line \u001b[0;36m7\n\u001b[1;32m 4\u001b[0m high \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m\n\u001b[1;32m 5\u001b[0m data \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marange(\u001b[39m-\u001b[39m\u001b[39m5\u001b[39m, \u001b[39m5\u001b[39m, \u001b[39m0.01\u001b[39m)\n\u001b[0;32m----> 7\u001b[0m pmf \u001b[39m=\u001b[39m duniform(data, low \u001b[39m=\u001b[39;49m low, high \u001b[39m=\u001b[39;49m high)\n\u001b[1;32m 8\u001b[0m cdf \u001b[39m=\u001b[39m puniform(data, low \u001b[39m=\u001b[39m low, high \u001b[39m=\u001b[39m high)\n\u001b[1;32m 9\u001b[0m ppf \u001b[39m=\u001b[39m quniform(data, low \u001b[39m=\u001b[39m low, high \u001b[39m=\u001b[39m high)\n","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/israel/problems.ipynb Cell 8\u001b[0m line \u001b[0;36m9\n\u001b[1;32m 5\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mduniform\u001b[39m(x, low \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m, high \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m):\n\u001b[1;32m 6\u001b[0m \u001b[39m \u001b[39m\u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m 7\u001b[0m \u001b[39m Calculates the point estimate of the uniform distribution\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[39m \"\"\"\u001b[39;00m\n\u001b[0;32m----> 9\u001b[0m result \u001b[39m=\u001b[39m uniform\u001b[39m.\u001b[39;49mpdf(x, low \u001b[39m=\u001b[39;49m \u001b[39m0\u001b[39;49m, scale \u001b[39m=\u001b[39;49m (high \u001b[39m-\u001b[39;49m low))\n\u001b[1;32m 11\u001b[0m \u001b[39mreturn\u001b[39;00m result\n","File \u001b[0;32m~/.local/lib/python3.11/site-packages/scipy/stats/_distn_infrastructure.py:1979\u001b[0m, in \u001b[0;36mrv_continuous.pdf\u001b[0;34m(self, x, *args, **kwds)\u001b[0m\n\u001b[1;32m 1958\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mpdf\u001b[39m(\u001b[39mself\u001b[39m, x, \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwds):\n\u001b[1;32m 1959\u001b[0m \u001b[39m \u001b[39m\u001b[39m\"\"\"Probability density function at x of the given RV.\u001b[39;00m\n\u001b[1;32m 1960\u001b[0m \n\u001b[1;32m 1961\u001b[0m \u001b[39m Parameters\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 1977\u001b[0m \n\u001b[1;32m 1978\u001b[0m \u001b[39m \"\"\"\u001b[39;00m\n\u001b[0;32m-> 1979\u001b[0m args, loc, scale \u001b[39m=\u001b[39m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_parse_args(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwds)\n\u001b[1;32m 1980\u001b[0m x, loc, scale \u001b[39m=\u001b[39m \u001b[39mmap\u001b[39m(asarray, (x, loc, scale))\n\u001b[1;32m 1981\u001b[0m args \u001b[39m=\u001b[39m \u001b[39mtuple\u001b[39m(\u001b[39mmap\u001b[39m(asarray, args))\n","\u001b[0;31mTypeError\u001b[0m: _parse_args() got an unexpected keyword argument 'low'"]}],"source":[]},{"cell_type":"code","execution_count":1,"id":"a99ee10c","metadata":{},"outputs":[{"ename":"NameError","evalue":"name 'np' is not defined","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/israel/problems.ipynb Cell 8\u001b[0m line \u001b[0;36m3\n\u001b[1;32m 32\u001b[0m result \u001b[39m=\u001b[39m norm\u001b[39m.\u001b[39mrvs(size \u001b[39m=\u001b[39m n, loc \u001b[39m=\u001b[39m mean, scale \u001b[39m=\u001b[39m std)\n\u001b[1;32m 34\u001b[0m \u001b[39mreturn\u001b[39;00m result\n\u001b[0;32m---> 36\u001b[0m np\u001b[39m.\u001b[39mrandom\u001b[39m.\u001b[39mseed(\u001b[39m42\u001b[39m)\n\u001b[1;32m 38\u001b[0m mean \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\n\u001b[1;32m 39\u001b[0m std \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m\n","\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"]}],"source":["from scipy.stats import norm\n","\n","\n","def dnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the density of the normal distribution\n"," \"\"\"\n"," result = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the cumulative of the normal distribution\n"," \"\"\"\n"," result = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result\n","\n","def qnorm(p, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the quantile function from the normal distribution\n"," \"\"\"\n"," result = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result\n","\n","def rnorm(n, mean = 0, std = 1):\n"," \"\"\"\n"," Generates random variables from the normal distribution\n"," \"\"\"\n"," result = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/notebook/solutions.ipynb b/notebook/solutions.ipynb index dfd430e6..0a4580fc 100644 --- a/notebook/solutions.ipynb +++ b/notebook/solutions.ipynb @@ -1 +1 @@ -{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution solutions"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Normal distribution"]},{"cell_type":"code","execution_count":1,"id":"31cfe823","metadata":{},"outputs":[],"source":["from scipy.stats import norm\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the density of the normal distribution\n"," \"\"\"\n"," result = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the cumulative of the normal distribution\n"," \"\"\"\n"," result = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result\n","\n","def qnorm(p, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the quantile function from the normal distribution\n"," \"\"\"\n"," result = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result\n","\n","def rnorm(n, mean = 0, std = 1):\n"," \"\"\"\n"," Generates random variables from the normal distribution\n"," \"\"\"\n"," result = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result"]},{"cell_type":"code","execution_count":2,"id":"69fd676b","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"4d723eed","metadata":{},"source":["## Uniform distribution"]},{"cell_type":"code","execution_count":3,"id":"6aa7367d","metadata":{},"outputs":[],"source":["from scipy.stats import uniform\n","\n","#Uniforme\n","def dunif(x, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the point estimate of the uniform distribution\n"," \"\"\"\n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def punif(q, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the cumulative of the uniform distribution\n"," \"\"\"\n"," result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def qunif(p, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the quantile function from the uniform distribution\n"," \"\"\"\n"," result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def runif(n, low = 0, high = 1):\n"," \"\"\"\n"," Generates random variables from the uniform distribution\n"," \"\"\"\n"," result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":4,"id":"3a17023b","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["np.random.seed(42)\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"9248718ffe6ce6938b217e69dbcc175ea21f4c6b28a317e96c05334edae734bb"},"kernelspec":{"display_name":"Python 3.9.12 ('ML-BOOTCAMP')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution solutions"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Normal distribution"]},{"cell_type":"code","execution_count":1,"id":"31cfe823","metadata":{},"outputs":[],"source":["from scipy.stats import norm\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the density of the normal distribution\n"," \"\"\"\n"," result = norm.pdf(x, loc = mean, scale = std)\n","\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the cumulative of the normal distribution\n"," \"\"\"\n"," result = norm.cdf(x = x, loc = mean, scale = std)\n","\n"," return result\n","\n","def qnorm(p, mean = 0, std = 1):\n"," \"\"\"\n"," Calculates the quantile function from the normal distribution\n"," \"\"\"\n"," result = norm.ppf(q = p, loc = mean, scale = std)\n","\n"," return result\n","\n","def rnorm(n, mean = 0, std = 1):\n"," \"\"\"\n"," Generates random variables from the normal distribution\n"," \"\"\"\n"," result = norm.rvs(size = n, loc = mean, scale = std)\n","\n"," return result"]},{"cell_type":"code","execution_count":2,"id":"69fd676b","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"4d723eed","metadata":{},"source":["## Uniform distribution"]},{"cell_type":"code","execution_count":3,"id":"6aa7367d","metadata":{},"outputs":[],"source":["from scipy.stats import uniform\n","\n","#Uniforme\n","def dunif(x, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the point estimate of the uniform distribution\n"," \"\"\"\n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def punif(q, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the cumulative of the uniform distribution\n"," \"\"\"\n"," result = uniform.cdf(q, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def qunif(p, low = 0, high = 1):\n"," \"\"\"\n"," Calculates the quantile function from the uniform distribution\n"," \"\"\"\n"," result = uniform.ppf(p, loc = low, scale = (high - low))\n","\n"," return result\n","\n","def runif(n, low = 0, high = 1):\n"," \"\"\"\n"," Generates random variables from the uniform distribution\n"," \"\"\"\n"," result = uniform.rvs(loc = low, scale = (high - low), size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":1,"id":"3a17023b","metadata":{},"outputs":[{"ename":"NameError","evalue":"name 'np' is not defined","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)","\u001b[1;32m/workspaces/probability-distribution-exercises-project-with-python-ds-2023/notebook/solutions.ipynb Cell 7\u001b[0m line \u001b[0;36m1\n\u001b[0;32m----> 1\u001b[0m np\u001b[39m.\u001b[39mrandom\u001b[39m.\u001b[39mseed(\u001b[39m42\u001b[39m)\n\u001b[1;32m 3\u001b[0m low \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\n\u001b[1;32m 4\u001b[0m high \u001b[39m=\u001b[39m \u001b[39m1\u001b[39m\n","\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"]}],"source":["np.random.seed(42)\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"9248718ffe6ce6938b217e69dbcc175ea21f4c6b28a317e96c05334edae734bb"},"kernelspec":{"display_name":"Python 3.9.12 ('ML-BOOTCAMP')","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5} diff --git a/ryan/problems.ipynb b/ryan/problems.ipynb new file mode 100644 index 00000000..9bb8d1b1 --- /dev/null +++ b/ryan/problems.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Probability distribution problems"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Binomial distribution\n","\n","In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, for example, when you flip a coin it can by either head or tails."]},{"cell_type":"code","execution_count":1,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Define all the probability functions related to this distribution\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the point estimate of the binomial distribution\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the cumulative of the binomial distribution\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calculates the quantile function from the binomial distribution\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Generates random variables from the binomial distribution\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":2,"id":"6cf6313a","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n","Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n","Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n","Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n"]}],"source":["# Binomial(10, 0.2) distribution where n = 10 is the number of trials and p = 0.2 is the probability of success in a single trial.\n","import numpy as np\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":3,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Exercise 1\n","\n","Write the above functions but for both normal and uniform distributions."]},{"cell_type":"code","execution_count":1,"id":"98d5f012","metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAd4AAAKxCAYAAAD91M3RAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABrj0lEQVR4nO3deVxU5f4H8M+AMKDCuCAgOgoqpuZCgiDaokVimWXdW7QpktmGpnHvVSmTyhItLUpJyzbLTMtyKb2WUbaJPxP15m6kCIKD4DKDqAPOnN8fTzOIrIPMObN83q/Xec3hcGbmy0R+OM95FpUkSRKIiIhIFh5KF0BEROROGLxEREQyYvASERHJiMFLREQkIwYvERGRjBi8REREMmLwEhERyaiF0gU0htlsRlFREfz8/KBSqZQuh4iIqAZJklBWVoaQkBB4eNR9XesUwVtUVAStVqt0GURERA0qKChA586d6/y+UwSvn58fAPHD+Pv7K1wNERFRTQaDAVqt1ppZdXGK4LU0L/v7+zN4iYjIoTV0S5Sdq4iIiGTE4CUiIpJRk4I3MzMToaGh8PHxQUxMDLZv396o561cuRIqlQpjxoxpytsSERE5PZuDd9WqVUhJSUFaWhp27tyJAQMGID4+HidPnqz3eXl5efj3v/+NG264ocnFEhEROTuVrevxxsTEYNCgQVi0aBEAMcZWq9Vi8uTJmDFjRq3PMZlMuPHGG/HII4/gl19+wdmzZ7F27do638NoNMJoNFq/tvQU0+v17FxFdDXOnQO2bgXy84HyciAgAOjbF+jXD6hn3CERNcxgMECj0TSYVTb9n1ZRUYGcnBzExcVVvYCHB+Li4pCdnV3n81566SUEBgZiwoQJjXqf9PR0aDQa68YxvERXQZKAH38E7rwTaNsWiI8HJk4Epk4FHn4YiIgAOnYEUlOBoiKlqyVyeTYFb2lpKUwmE4KCgqodDwoKgk6nq/U5v/76K95//30sXbq00e+TmpoKvV5v3QoKCmwpk4gsjh4F7rgDuPlm4OuvgUuXgNBQYNQo4L77gGHDgFatgJMngblzgR49gHnzgMpKpSsncll2HcdbVlaGsWPHYunSpQgICGj089RqNdRqtR0rI3IDa9YAiYlAWRng5SWucidNAnr3rn5eRQWwcSPw6qtAdjYwY4YI6c8/B0JClKmdyIXZFLwBAQHw9PREcXFxtePFxcUIDg6ucf5ff/2FvLw8jB492nrMbDaLN27RAocOHUL37t2bUjcR1WfePBGgADB0KPDee0CvXrWf6+0NjBkD3HUX8MknwNNPA7/9BkRFAd99J+4BE1Gzsamp2dvbG5GRkcjKyrIeM5vNyMrKQmxsbI3ze/XqhT179mD37t3W7c4778Tw4cOxe/du3rslsoeZM6tCd8oUcX+3rtC9nEoFjBsH/P47cO21wIkTwE03ATk59q2XyM3Y3NSckpKCxMREREVFITo6GhkZGSgvL0dSUhIAYNy4cejUqRPS09Ph4+ODvlf8tdymTRsAqHGciJrBG28Ar7wi9ufNA6ZNs/01wsOBn38GbrsN2L5dPGZnA2ydImoWNgdvQkICSkpKMGvWLOh0OkRERGDTpk3WDlf5+fn1LodERHby+edASorYb2roWrRrB2zeDAwfDuzcCYwcKYYhdejQPLUSuTGbx/EqobFjo4jc1h9/ADExwMWLogPVW2+JpuOrpdMBsbFAXp4I4c2bAU/Pq39dIhdkl3G8ROSAysqAe+8VoTtyJJCR0TyhCwDBwaLHc6tW4l7xiy82z+sSuTEGL5Gze+IJ4PBhQKsFli9v/ivS3r2Bd98V+y+/DHz/ffO+PpGbYfASObMvvwRWrBBhu2oV0L69fd7nwQeBxx4Ts2A98ghgMNjnfYjcAIOXyFmdOgUkJ4v9GTPEvVh7ev11oFs3oKAA+M9/7PteRC6MwUvkrJ55BiguFk3Bzz9v//dr1Qp4/32x/+67wGXj+Ymo8Ri8RM7o++/FLFMeHsCHHwJyTbE6bBjw1FNif9IkzulM1AQMXiJnc+mSmJEKEOEXEyPv+7/yihjPe/AgsHChvO9N5AIYvETOZskSYP9+0ZHqhRfkf/82bYD0dLH/wgtirC8RNRqDl8iZnDoFzJol9l9+Wayvq4SkJLGIQlmZWMeXiBqNwUvkTGbPBs6cAfr1Ax59VLk6PDyqmpmXLQP27lWuFiInw+AlchYFBcDixWJ/wQKghV2X027Y4MHAP/4hxvbOnKlsLUROhMFL5CxeflksWn/TTUBcnNLVCLNni6vfdeuAbduUrobIKTB4iZzBX38BH3wg9l9+ufnmYr5avXsD48eL/dRUcfVLRPVi8BI5g5deEsOIRo4Err9e6WqqS0sT44i3bBEbEdWLwUvk6A4eFIsfAKJp19F06VLV0euVV5SthcgJMHiJHN28eYDZDNx1lxjC44imTROdvbKyeK+XqAEMXiJHlp9fdbX77LPK1lKfLl2AsWPFPq96ierF4CVyZK+/Lu7t3nwzEB2tdDX1mzFD9HD+5hvgf/9Tuhoih8XgJXJUpaXA0qVif8YMZWtpjJ49gfvuE/tz5ihbC5EDY/ASOapFi4Dz54GBAx1n3G5DLM3hq1cDR48qWwuRg2LwEjmi8vKqKRlTUx1n3G5D+vUDbr1VdAbjykVEtWLwEjmi5cuB06eBbt2Au+9WuhrbpKSIx/feAwwGZWshckAMXiJHI0nAW2+J/cmTAU9PZeuxVXy8mNGqrAx4/32lqyFyOAxeIkeTlSXW223dWiy/52xUKmDqVLH/1luAyaRoOUSOhsFL5GjefFM8JiUBGo2ytTTV2LFA+/ZAXh6wdq3S1RA5FAYvkSPJzQU2bBD7kyYpW8vV8PUFnnxS7L/xhrK1EDkYBi+RI1m0SNzjvf12MS7WmT31FODlBfz2G7B7t9LVEDkMBi+RozAYqpb+mzJF2VqaQ8eOwD33iP3Fi5WthciBMHiJHMWyZaIncK9eYiysK7A0N3/6KaDXK1sLkYNg8BI5AkkCliwR+5MmOc+EGQ258UagTx8xIcgnnyhdDZFDYPASOYLffhNDiFq2BB5+WOlqmo9KVXXVu3ix+AODyM0xeIkcwTvviMcHHnDeIUR1GTtW/EGxfz/wyy9KV0OkuCYFb2ZmJkJDQ+Hj44OYmBhs3769znO/+uorREVFoU2bNmjVqhUiIiLwCZuciKqcOgV88YXYf/xxZWuxB42m6ir+7beVrYXIAdgcvKtWrUJKSgrS0tKwc+dODBgwAPHx8Th58mSt57dr1w7PPfccsrOz8ccffyApKQlJSUn49ttvr7p4Ipfw8ceA0Qhcdx0QFaV0NfZhaW7+6iuguFjZWogUppIk2266xMTEYNCgQVi0aBEAwGw2Q6vVYvLkyZjRyDVDBw4ciFGjRmH27Nm1ft9oNMJoNFq/NhgM0Gq10Ov18Pf3t6VcIscmSWJe40OHROcqV7zitYiNBbZtE2v1pqYqXQ1RszMYDNBoNA1mlU1XvBUVFcjJyUHcZWuDenh4IC4uDtnZ2Q0+X5IkZGVl4dChQ7jxxhvrPC89PR0ajca6abVaW8okch4//yxCt3Vr4MEHla7Gvix/VLz/vlg2kMhN2RS8paWlMJlMCAoKqnY8KCgIOp2uzufp9Xq0bt0a3t7eGDVqFBYuXIhb6xmnmJqaCr1eb90KCgpsKZPIeVg6VT34IODnp2wt9nbvveJn/Osv8QcHkZtqIceb+Pn5Yffu3Th37hyysrKQkpKCbt26YdiwYbWer1aroVar5SiNSDmlpcCXX4p9V25itmjVSvTafvddsVZvHf//E7k6m654AwIC4OnpieIrOkcUFxcjODi47jfx8ECPHj0QERGBf/3rX/jnP/+J9PT0plVM5Co+/hioqBAdqgYOVLoaeTz6qHhcvRo4c0bZWogUYlPwent7IzIyEllZWdZjZrMZWVlZiI2NbfTrmM3map2niNyOJAEffij2J0xQthY5RUUB/fuLXtwrVihdDZEibB5OlJKSgqVLl2LZsmU4cOAAnnzySZSXlyPp7wW7x40bh9TLeiymp6dj8+bNOHLkCA4cOIAFCxbgk08+wcOuNDsPka1ycoC9ewEfH+D++5WuRj4qVdUfGkuXciYrcks23+NNSEhASUkJZs2aBZ1Oh4iICGzatMna4So/Px8eHlV5Xl5ejqeeegrHjx+Hr68vevXqheXLlyMhIaH5fgoiZ/PRR+Lx7ruBNm2UrER+Dz8MTJsG/O9/wM6dQGSk0hURycrmcbxKaOzYKCKncPEiEBIi7nF++y0wYoTSFcnvgQeAlSvFxBqczYpchF3G8RJRM1i/XoRu587ALbcoXY0yLJ2sPv0UOH9e2VqIZMbgJZKbpZk5MRHw9FS0FMUMHw6EhQEGg+jhTORGGLxEciosFM3LgAhed+XhATzyiNh//31layGSGYOXSE6ffCKmS7z+eiA8XOlqlJWYKHo5//wzcOSI0tUQyYbBSyQXSapqZv57+J1b02oBy7zvH3+sbC1EMmLwEsll2zaxIELLlmLeYgLGjxePy5Zx4QRyGwxeIrlYZqr65z9df0GExhozBvD3B/LyuHACuQ0GL5Eczp8HVq0S+2xmrtKyJWCZTMfSDE/k4hi8RHJYs0YMnQkNBepZi9otWZqbV68Gzp1TtBQiOTB4ieRgaWYeP14MpaEqsbGih3d5Ocf0klvgvwBE9nbsGPDDD2Lfncfu1kWlqrrqZXMzuQEGL5G9ffyxGEo0fLhoaqaaxo4VAfzTT8DRo0pXQ2RXDF4iezKbOXa3MbTaqnmrOaaXXByDl8iefv1VzMrk5wfcc4/S1Tg2juklN8HgJbInS6eq++4DWrVSthZHd/fd4g+Uo0eBX35Ruhoiu2HwEtnLuXPAF1+IfTYzN4xjeslNMHiJ7OWLL8QQmfBwYMgQpatxDpbm5i++4JheclkMXiJ7sVy1jR8veuxSw4YMAXr0EH+wfPml0tUQ2QWDl8ge/vpLzD3s4QGMG6d0Nc6DY3rJDTB4iezBEhq33gp07qxoKU7HMqZ3yxaO6SWXxOAlam5msxgSA1RdvVHjdenCMb3k0hi8RM3thx+AggKgTRux7B3ZjmN6yYUxeImam2Xs7v33Az4+ytbirDiml1wYg5eoOZ09C3z1ldjn2N2mu3xMr6XZnshFMHiJmtOqVcDFi0CfPsCgQUpX49wszc2ff84xveRSGLxEzcnSzJyUxLG7V2vIkKp1ei0zgBG5AAYvUXM5cAD4v/8DPD2Bhx9Wuhrnp1IBjzwi9j/4QNlaiJoRg5eouViudm+/HQgOVrYWVzFunJiE5NdfgcOHla6GqFkweImaw6VLwCefiH3LVRpdvZAQYORIsc+ZrMhFMHiJmsOmTYBOB3ToAIwapXQ1rsXyh8yyZYDJpGwtRM2AwUvUHCzNzA8/DHh5KVuLqxk9GmjfHigqAr77TulqiK4ag5foapWWAl9/LfY5drf5eXtXdVZjJytyAU0K3szMTISGhsLHxwcxMTHYvn17necuXboUN9xwA9q2bYu2bdsiLi6u3vOJnM6nnwKVlUBkJNCvn9LVuCbLHzTr1ok/dIicmM3Bu2rVKqSkpCAtLQ07d+7EgAEDEB8fj5MnT9Z6/pYtW/DAAw/gxx9/RHZ2NrRaLUaMGIHCwsKrLp7IIVw+dpfsY8AAYOBA8QfOihVKV0N0VVSSJEm2PCEmJgaDBg3CokWLAABmsxlarRaTJ0/GjBkzGny+yWRC27ZtsWjRIoyrY51So9EIo9Fo/dpgMECr1UKv18Pf39+Wconsa9cuEQje3sCJE0C7dkpX5LoyM4FJk4D+/YHduzlBCTkcg8EAjUbTYFbZdMVbUVGBnJwcxMXFVb2Ahwfi4uKQnZ3dqNc4f/48Kisr0a6ef6DS09Oh0Wism1artaVMIvlYrnbHjGHo2tsDDwBqNfDHH+IPHiInZVPwlpaWwmQyISgoqNrxoKAg6HS6Rr3G9OnTERISUi28r5Samgq9Xm/dCgoKbCmTSB5Go7i/C7CZWQ7t2lUts2j5g4fICcnaq3nu3LlYuXIl1qxZA596lktTq9Xw9/evthE5nPXrgdOngU6dgFtvVboa92AZ0/vpp2IxCiInZFPwBgQEwNPTE8XFxdWOFxcXI7iBKfLmz5+PuXPn4rvvvkP//v1tr5TI0SxdKh4TE8X8zGR/t9wCaLXAmTOihzORE7IpeL29vREZGYmsrCzrMbPZjKysLMTGxtb5vFdffRWzZ8/Gpk2bEBUV1fRqiRzF0aPA5s1i/9FHla3FnXh6Vi0XyOZmclI2NzWnpKRg6dKlWLZsGQ4cOIAnn3wS5eXlSPr7Hte4ceOQmppqPX/evHl4/vnn8cEHHyA0NBQ6nQ46nQ7nuL4mObP33hOPI0YAYWHK1uJuLMH73XdAfr6ipRA1hc3Bm5CQgPnz52PWrFmIiIjA7t27sWnTJmuHq/z8fJw4ccJ6/uLFi1FRUYF//vOf6Nixo3WbP39+8/0URHKqrKy62po4Udla3FG3bsDNNwOSVPUHEJETsXkcrxIaOzaKSBZr1wJ33y0WRDh+XIzhJXl9/jmQkCBWLzp2DGjRQumKiOwzjpeIUNWpKimJoauUMWPEHz5FRcA33yhdDZFNGLxEtsjPB/77X7HPTlXK8fauGjv9zjvK1kJkIwYvkS0++EDcWxw+HAgPV7oa92a5v/7tt0BenqKlENmCwUvUWCYT8P77Yp+dqpTXowcQFyf+ELI0/xM5AQYvUWNt2iQ6U7VvLzpXkfIef1w8fvCB6G1O5AQYvESNtWSJeBw3DqhnylOS0V13AUFBgE4npvAkcgIMXqLGOHoU2LBB7D/xhLK1UBUvr6r5m9nJipwEg5eoMRYvFvcSR4wAevZUuhq63MSJYm3ezZuBv/5SuhqiBjF4iRpy4UJVp6rkZGVroZrCwsQfREDV7QAiB8bgJWrIqlVi+b+uXYFRo5SuhmozaZJ4fO89oLxc2VqIGsDgJaqPJAGLFon9J5/k8n+O6rbbxBzOZ8+KtXqJHBiDl6g+27cDOTmAWg1MmKB0NVQXT8+qq9633hJ/MBE5KAYvUX0sV7v33w8EBChbC9UvKQlo2RLYtw/YskXpaojqxOAlqsvJk2IVHICdqpxBmzZAYqLYf+stRUshqg+Dl6guS5cCFRVAdDQwaJDS1VBjWJqb16/n/M3ksBi8RLUxGquamSdPVrYWarw+fcT8zWYz8PbbSldDVCsGL1FtPvtMTEPYqZNYcJ2ch+UPpffeA86fV7YWoloweImuJEnA66+L/aefFtMSkvMYNUpMqnHmDLBsmdLVENXA4CW60vffA3v2AK1acfk/Z+TpCUydKvYXLBDLORI5EAYv0ZUWLBCPEyYAbdsqWws1zYQJQLt2Yu7mNWuUroaoGgYv0eX27gW+/Rbw8ACmTFG6GmqqVq2Ap54S+6+9xgk1yKEweIku98Yb4vHuu8UUhOS8Jk8WM45t3w788ovS1RBZMXiJLIqKgOXLxf6//qVsLXT1AgOB8ePF/quvKloK0eUYvEQW8+eLCTOuvx6IjVW6GmoO//qXWKt3wwYxlSSRA2DwEgFAaSnwzjti/7nnlK2Fmk94uLhtAIh7vUQOgMFLBAAZGWKyhchIID5e6WqoOU2fLh6XLweOHlW2FiIweIkAvb5qesjnnhNNk+Q6oqOBESPEeN45c5SuhojBS4TMTBG+114L3HWX0tWQPaSlicePPgKOHVO0FCIGL7m3c+eqhhClporxu+R6hgwBbrkFuHQJmDtX6WrIzfFfGXJvCxeKjlU9enAxBFdnuep9/32goEDZWsitMXjJfZ09WzW+84UXgBYtlKyG7O2GG4Bhw4DKSl71kqIYvOS+FiwQ4dunD3D//UpXQ3KwXPUuXcoezqSYJgVvZmYmQkND4ePjg5iYGGzfvr3Oc/ft24d//OMfCA0NhUqlQkZGRlNrJWo+JSViCBEAzJ4tVrQh1zdsGBAXJ656LSFMJDObg3fVqlVISUlBWloadu7ciQEDBiA+Ph4nT56s9fzz58+jW7dumDt3LoKDg6+6YKJmMW+e6Fg1cGDVBAvkHizNzMuXA3/8oWwt5JZUkmTbsh0xMTEYNGgQFv097tFsNkOr1WLy5MmYMWNGvc8NDQ3F1KlTMdWyVmYdjEYjjEaj9WuDwQCtVgu9Xg9/f39byiWqqbBQdKa6eBHYuBG47TalKyK5JSQAn38OjBoFfPON0tWQizAYDNBoNA1mlU1XvBUVFcjJyUFcXFzVC3h4IC4uDtnZ2U2v9grp6enQaDTWTavVNttrE+HZZ0XoXn89MHKk0tWQEl5+WXSm27CBKxeR7GwK3tLSUphMJgQFBVU7HhQUBJ1O12xFpaamQq/XW7cCdv2n5rJjB/Dxx2L/9dc5S5W7Cg8HHn1U7E+fzvV6SVYO2atZrVbD39+/2kZ01SQJSEkR+w8/DAwapGw9pKxZs4CWLYHsbGDlSqWrITdiU/AGBATA09MTxcXF1Y4XFxez4xQ5vjVrRLOiry/n7CWgY0dx2wEA/vMf0dmOSAY2Ba+3tzciIyORlZVlPWY2m5GVlYVYrl9KjsxoFP+4AsC//w2w3wABYr3esDDR4S49XelqyE3Y3NSckpKCpUuXYtmyZThw4ACefPJJlJeXIykpCQAwbtw4pKamWs+vqKjA7t27sXv3blRUVKCwsBC7d+9Gbm5u8/0URA1ZsAA4ckRc5UybpnQ15Ch8fMS9fgCYPx/46y9l6yG3YPMceQkJCSgpKcGsWbOg0+kQERGBTZs2WTtc5efnw+OyieaLiopw3XXXWb+eP38+5s+fj5tuuglbtmy5+p+AqCFHjohJMgCxGHrr1srWQ47lrrvEpBrffy/6AKxbp3RF5OJsHserhMaOjSKqQZLEWM3//he4+Wbxjyt7MtOV9u8H+vcXa/auWwfceafSFZETsss4XiKn89VXInS9vYG332boUu369BH3ewHgqacAg0HZesilMXjJdZ09Czz9tNifPh245hpFyyEHl5YGdO8uOlpZejsT2QGDl1zXM88ARUViesjLOvwR1aplS+Cdd8T+228DW7cqWw+5LAYvuaYNG4CPPhJNyx9+KMbuEjXklluApCTRN+CRR4Dz55WuiFwQg5dcz5kzwMSJYv+ZZ8SczESNNX++GHZ26BCHnpFdMHjJtUgSkJwMnDgB9OwpJsMnskW7dqK1BAAyM4FNmxQth1wPg5dcy4cfAp99Jha2X7aMTczUNCNGAJMni/2kJKC0VNl6yKUweMl17N8PTJok9mfPBgYPVrYecm7z5gG9ewM6HZCYCJjNSldELoLBS67h/HmxuPmFC8Ctt4rhQ0RXw9dXtJ74+AAbN3JhDWo2DF5yfpIEPP44sHcvEBQEfPIJ4MFfbWoGAwaIoUWAWEbw+++VrYdcAv91Iue3YAGwfLm4r7tihQhfouaSlARMmCD+wHvgAeDYMaUrIifH4CXntmlTVbPyG2+I+ZiJmtvChcB114lOVnfcAej1SldETozBS85r717g/vtFp5cJE6o6VhE1N19fYP16Mb53717Rn+DSJaWrIifF4CXndOwYEB8vrjyuv16Mt+QCCGRPnTsDX38tppb89lvxh57jL+5GDojBS86ntFSEblERcO21Yhk3tVrpqsgdREaKfgQqlZjXOTWV4Us2Y/CSczlzBrjtNjGdn1Yr7vG2a6d0VeRO7roLWLJE7M+bx2FGZDMGLzmP06eBuDhgxw6gfXvR3Ne5s9JVkTt67DHg9dfF/syZwGuvKVsPORUGLzmH0lKxcszOnUCHDsCPP4pZhYiU8swzwEsvif1p00QAs9mZGoHBS47vr7+AoUOB3bvFGN0tW4B+/ZSuigh4/nkgPV3sv/KKmN+ZU0tSAxi85Nj+7/+A2Fjg8GGgSxcRun36KF0VUZUZM8TsViqV6F1/zz3AuXNKV0UOjMFLjmv5cmD4cKCkBBg4ENi2DejVS+mqiGp68kng008Bb2/Ry37oUM5wRXVi8JLjMRqBp54Cxo4Vix7cfjvw009i8gIiR/XAA6JFJigI+OMPICpKLK5AdAUGLzmWAwfEhBiLF4umu1mzxIxBrVsrXRlRw2Jjgd9/Fy00paXAqFFASor4Y5Lobwxecgwmk1js4LrrxHChdu3E1cKLL4rFD4ichVYL/PYb8PTT4us33gAGDQK2b1e2LnIYDF5SnqUD1b//La4MbrtNNNWNHKl0ZURN4+MDvPmmaK0JCAD27AEGDwamTgUMBqWrI4UxeEk5J06IJdcGDxbNc35+wHvvARs2AJ06KV0d0dUbPRrYvx94+GExxvfNN4EePUQv6MpKpasjhTB4SX4nTojJB7p1Az76SBxLShJDhiZM4GIH5Fo6dAA++QT473+B8HDRSz85GejbF/jsM65y5IYYvCSfAwfEii7dugEZGcDFi6KJ+f/+D/jgAyA4WOkKiexn5Ehg3z5g0SIRxocPAw8+CPTsKa6Az59XukKSCYOX7OvCBWD1ajHdY58+YoKBixeBIUPEXMu//QZERytdJZE8vLzE1W5urphuMiAAOHpUHAsJEY+7dildJdmZSpIcf3JRg8EAjUYDvV4Pf39/pcuhhhiNYi7lzz4D1qwBysrEcQ8Pcc/r6afFxBhsUiZ3d/488OGHYsGFI0eqjvftC/zjH2Lr25f/rziJxmYVg5euniQBf/4JfP+9WKbvhx+A8vKq73fpIjqXPP642Cei6sxm8f/Ne++JP1YrKqq+16MHMGIEcPPNwLBhYmUuckgMXrIPSRIL0O/bJ8bbZmeL7dSp6ucFB4u/1h94QNzH9eBdDaJGOX0a+Ppr4Msvge++qz75hkolFgiJigIiI8XWvz/g66tcvWRl1+DNzMzEa6+9Bp1OhwEDBmDhwoWIruc+3RdffIHnn38eeXl5CA8Px7x583D77bc3+v0YvDIzm0XP42PHqrYjR0TY7tsH6PU1n6NWi2FBI0eKrX9/hi3R1SorA7KyxK2brCzx/9+VPDyAsDDRScuyde8uhuSFhABt27KpWiZ2C95Vq1Zh3LhxWLJkCWJiYpCRkYEvvvgChw4dQmBgYI3zt27dihtvvBHp6em44447sGLFCsybNw87d+5E3759m/WHcXsmkxgbWFkpmqouXhSrpJw7J5p+LfuWTa8XQxtKSsT0dpbHkyfrH2Po6SmGRfTvLzpJxcYCERFigngish+dTiwWsmMHkJMjtpKS+p/j4yMCOCRENFO3bVtza9NGXDW3bCk2y77lUa1meDeC3YI3JiYGgwYNwqJFiwAAZrMZWq0WkydPxowZM2qcn5CQgPLycnzzzTfWY4MHD0ZERASWLFlS63sYjUYYL2teMRgM0Gq1zRO8CQlVV2ySVLVwdX37tpxrz9ewhOrlW0VF1X5z3jXw9AQ6dwa6dq3a+vQBrr0WuOYa8T8iESlLkkTr1OHDop/F4cNiO3pU3BK68hbQ1WjRovrm5VXzmGXz9BRBbY+tsWw59/33m2XSnsYGbwtbXrSiogI5OTlITU21HvPw8EBcXByys7NrfU52djZSUlKqHYuPj8fatWvrfJ/09HS8+OKLtpTWeFlZzfvL6Mg8PcVsUK1bi61Vq6r91q0Bf38xnjAgQDxa9gMDxUpALWz69SAiualUVVezw4bV/P7FiyKALdvp08CZMzU3vV4M/btwQfS0tjxePrnHpUuuO9nHhQuyvp1N/7KWlpbCZDIhKCio2vGgoCAcPHiw1ufodLpaz9fpdHW+T2pqarWwtlzxNovMTNFZwfLX0OV/RdV1zFG+7+VVtXl7V/+6tmOWvzqJyD35+IgJa7p1a9rzKyurAtkSvJdvlZW1HzOZxPMtrXbNtTWWra1/tdwmtSeHvKRRq9VQ26spMyHBPq9LRORqLH/Es29Ns7Kp22lAQAA8PT1RXFxc7XhxcTGC65juLzg42KbziYiIXJlNwevt7Y3IyEhkZWVZj5nNZmRlZSE2NrbW58TGxlY7HwA2b95c5/lERESuzOam5pSUFCQmJiIqKgrR0dHIyMhAeXk5kpKSAADjxo1Dp06dkJ6eDgCYMmUKbrrpJixYsACjRo3CypUrsWPHDrz77rvN+5MQERE5AZuDNyEhASUlJZg1axZ0Oh0iIiKwadMmaweq/Px8eFw2ccKQIUOwYsUKzJw5E88++yzCw8Oxdu3aRo/hJSIiciWcMpKIiKgZ2GUcr1IsfxsYDAaFKyEiIqqdJaMaup51iuAt+3tZuWYby0tERGQnZWVl0Gg0dX7fKZqazWYzioqK4OfnB5ULTwhhmSikoKCATeo24OdmO35mTcPPrWnc5XOTJAllZWUICQmp1tfpSk5xxevh4YHOnTsrXYZs/P39XfqX0174udmOn1nT8HNrGnf43Oq70rXgum1EREQyYvASERHJiMHrQNRqNdLS0uw3T7WL4udmO35mTcPPrWn4uVXnFJ2riIiIXAWveImIiGTE4CUiIpIRg5eIiEhGDF4iIiIZMXiJiIhkxOB1cEajEREREVCpVNi9e7fS5Ti0vLw8TJgwAWFhYfD19UX37t2RlpaGiooKpUtzOJmZmQgNDYWPjw9iYmKwfft2pUtyaOnp6Rg0aBD8/PwQGBiIMWPG4NChQ0qX5VTmzp0LlUqFqVOnKl2K4hi8Dm7atGkICQlRugyncPDgQZjNZrzzzjvYt28f3njjDSxZsgTPPvus0qU5lFWrViElJQVpaWnYuXMnBgwYgPj4eJw8eVLp0hzWTz/9hOTkZGzbtg2bN29GZWUlRowYgfLycqVLcwq///473nnnHfTv31/pUhyDRA5r48aNUq9evaR9+/ZJAKRdu3YpXZLTefXVV6WwsDCly3Ao0dHRUnJysvVrk8kkhYSESOnp6QpW5VxOnjwpAZB++uknpUtxeGVlZVJ4eLi0efNm6aabbpKmTJmidEmK4xWvgyouLsbEiRPxySefoGXLlkqX47T0ej3atWundBkOo6KiAjk5OYiLi7Me8/DwQFxcHLKzsxWszLno9XoA4O9WIyQnJ2PUqFHVfufcnVOsTuRuJEnC+PHj8cQTTyAqKgp5eXlKl+SUcnNzsXDhQsyfP1/pUhxGaWkpTCYTgoKCqh0PCgrCwYMHFarKuZjNZkydOhVDhw5F3759lS7Hoa1cuRI7d+7E77//rnQpDoVXvDKaMWMGVCpVvdvBgwexcOFClJWVITU1VemSHUJjP7fLFRYWYuTIkbj33nsxceJEhSonV5ScnIy9e/di5cqVSpfi0AoKCjBlyhR8+umn8PHxUboch8K5mmVUUlKCU6dO1XtOt27dcN999+Hrr7+GSqWyHjeZTPD09MRDDz2EZcuW2btUh9LYz83b2xsAUFRUhGHDhmHw4MH46KOP6l2Q2t1UVFSgZcuWWL16NcaMGWM9npiYiLNnz2LdunXKFecEJk2ahHXr1uHnn39GWFiY0uU4tLVr1+Luu++Gp6en9ZjJZIJKpYKHhweMRmO177kTBq8Dys/Ph8FgsH5dVFSE+Ph4rF69GjExMejcubOC1Tm2wsJCDB8+HJGRkVi+fLnb/o9dn5iYGERHR2PhwoUARNNply5dMGnSJMyYMUPh6hyTJEmYPHky1qxZgy1btiA8PFzpkhxeWVkZjh07Vu1YUlISevXqhenTp7t1Mz3v8TqgLl26VPu6devWAIDu3bszdOtRWFiIYcOGoWvXrpg/fz5KSkqs3wsODlawMseSkpKCxMREREVFITo6GhkZGSgvL0dSUpLSpTms5ORkrFixAuvWrYOfnx90Oh0AQKPRwNfXV+HqHJOfn1+NcG3VqhXat2/v1qELMHjJhWzevBm5ubnIzc2t8QcKG3aqJCQkoKSkBLNmzYJOp0NERAQ2bdpUo8MVVVm8eDEAYNiwYdWOf/jhhxg/frz8BZFTY1MzERGRjNjrhIiISEYMXiIiIhkxeImIiGTE4CUiIpIRg5eIiEhGDF4iIiIZMXiJiIhkxOAlIiKSEYOXiIhIRgxeIiIiGTF4iYiIZMTgJSIikhGDl4iISEYMXiIiIhkxeImIiGTE4CUiIpJRC6ULaAyz2YyioiL4+flBpVIpXQ4REVENkiShrKwMISEh8PCo+7rWKYK3qKgIWq1W6TKIiIgaVFBQgM6dO9f5facIXj8/PwDih/H391e4GiIiopoMBgO0Wq01s+riFMFraV729/dn8BIRkUNr6JYoO1cRERHJiMFLREQkI5uD9+eff8bo0aMREhIClUqFtWvXNvicLVu2YODAgVCr1ejRowc++uijJpRKRETk/GwO3vLycgwYMACZmZmNOv/o0aMYNWoUhg8fjt27d2Pq1Kl49NFH8e2339pcLBERkbOzuXPVbbfdhttuu63R5y9ZsgRhYWFYsGABAKB379749ddf8cYbbyA+Pr7W5xiNRhiNRuvXBoPB1jKJiJxSRQVQVlZ9O3cOuHABMBob3i5dAkwmsZnN1R8b2jebRQ2SVFWPZd/WY1fzGnJbtQqQc8Sq3Xs1Z2dnIy4urtqx+Ph4TJ06tc7npKen48UXX7RzZURE9mc0AsePA/n5QEEBcPIkUFoKlJRU386cESFbWal0xe7n4kV538/uwavT6RAUFFTtWFBQEAwGAy5cuABfX98az0lNTUVKSor1a8vYKCIiR2Q0AocPAwcOAAcPiscjR0TY6nRNe00fH8DPT2ytWwMtWwJqdcNbixaAp6fYPDxs21epxAZUPV6+b+uxpryGEjp2lPf9HHIcr1qthlqtVroMIqIaLl4Edu8Gfv+9ajt8uKqZtja+vkCXLkDnzkBQENChQ9UWECAe27WrHrReXrL9SCQzuwdvcHAwiouLqx0rLi6Gv79/rVe7RESOxGgEtm0DsrLEtn27uI96JY0G6N1bbL16AeHhQNeuInDbt1f+qo4ch92DNzY2Fhs3bqx2bPPmzYiNjbX3WxMRNUlJCbB+PfDVV8CPP4qOTZcLDAQGDararrsOCA5muFLj2By8586dQ25urvXro0ePYvfu3WjXrh26dOmC1NRUFBYW4uOPPwYAPPHEE1i0aBGmTZuGRx55BD/88AM+//xzbNiwofl+CiKiq3T2LLBypejh+vPP1ZuOAwOBW24R2803A6GhDFlqOpuDd8eOHRg+fLj1a0snqMTERHz00Uc4ceIE8vPzrd8PCwvDhg0b8Mwzz+DNN99E586d8d5779U5lIiISC5mM7BlC/DBB8CXX1bv3TpwIHD33cCddwL9+jFoqfmoJEmpkVONZzAYoNFooNfruUgCEV21CxeAjz8G3ngDOHSo6vi11wJJScA//iGuaols0discshezURE9nD2LPDmm8CiRWIsLQD4+wMPPgg88ggQFcUrW7I/Bi8Rubxz54C33gJee02ELyB6HE+dCkyYIIbwEMmFwUtELstkAt59F3jhBTFjFCCak2fNAu65R0w2QSQ3/toRkUvauhVIThaTXQBA9+7Aiy8C998vZmkiUgqDl4hcyunTQEoKsGyZ+LpNG2D2bODxxzkbFDkGBi8RuYwNG4CJE4ETJ0QnqQkTgDlzxJSMRI6CwUtETk+vB555BvjwQ/F1r15if/BgZesiqg2Dl4ic2q5dwD//KVYDUqlEM/Ps2WJhAiJHxOAlIqckScDSpcDTT4uFDLp2BZYvB66/XunKiOrH4CUip3Phgugs9ckn4us77hAzUbVtq2xdRI3hoXQBRES2OHlSLFTwySdiWNDcucC6dQxdch684iUip7F/PzBqFJCXJ4J29WoRwkTOhMFLRE7hhx/EbFN6vZgMY8MG4JprlK6KyHZsaiYih7d+PXDbbSJ0hw4Ftm1j6JLzYvASkUP77DNxpVtRAYwZA3z/PRAQoHRVRE3H4CUih7V0KfDQQ2Kxg4cfBr74AvDxUboqoqvD4CUih/Tee8Bjj4nxuk88IeZe5mpC5AoYvETkcD79VIQuIKaCfPttwIP/WpGL4K8yETmUr74CEhPFle5TTwELFoipIIlcBYOXiBzGpk1ivVyTCRg/Hli4kKFLrofBS0QOISdHLHZQWQkkJIh7vGxeJlfEX2siUlxenpiRqrwcuPXWqukgiVwRg5eIFHXmjJgco7gYGDBATAPp5aV0VUT206TgzczMRGhoKHx8fBATE4Pt27fXe35GRgauueYa+Pr6QqvV4plnnsHFixebVDARuQ6jUUyKcfAg0LmzmAbS31/pqojsy+bgXbVqFVJSUpCWloadO3diwIABiI+Px8mTJ2s9f8WKFZgxYwbS0tJw4MABvP/++1i1ahWeffbZqy6eiJyXJAGTJwM//yzCduNGoFMnpasisj+bg/f111/HxIkTkZSUhD59+mDJkiVo2bIlPvjgg1rP37p1K4YOHYoHH3wQoaGhGDFiBB544IEGr5KJyLW9846YmUqlAlatAvr1U7oiInnYFLwVFRXIyclBXFxc1Qt4eCAuLg7Z2dm1PmfIkCHIycmxBu2RI0ewceNG3H777XW+j9FohMFgqLYRkev45RdxtQsA6enAyJHK1kMkJ5smYCstLYXJZEJQUFC140FBQTh48GCtz3nwwQdRWlqK66+/HpIk4dKlS3jiiSfqbWpOT0/Hiy++aEtpROQkCgrEsKFLl8SwoWnTlK6ISF5279W8ZcsWzJkzB2+//TZ27tyJr776Chs2bMDs2bPrfE5qair0er11KygosHeZRCQDo1GsNHTypOjB/P77nCCD3I9NV7wBAQHw9PREcXFxtePFxcUIDg6u9TnPP/88xo4di0cffRQA0K9fP5SXl+Oxxx7Dc889B49aRsir1Wqo1WpbSiMiJ/DvfwM7dgDt2wNr1wKtWildEZH8bLri9fb2RmRkJLKysqzHzGYzsrKyEBsbW+tzzp8/XyNcPf8eGS9Jkq31EpGT+vJLYNEisf/JJ0BoqKLlECnG5kW2UlJSkJiYiKioKERHRyMjIwPl5eVISkoCAIwbNw6dOnVCeno6AGD06NF4/fXXcd111yEmJga5ubl4/vnnMXr0aGsAE5FrO3IEmDBB7E+bJibMIHJXNgdvQkICSkpKMGvWLOh0OkRERGDTpk3WDlf5+fnVrnBnzpwJlUqFmTNnorCwEB06dMDo0aPxyiuvNN9PQUQOq6JCLHyg1wNDhgAvv6x0RUTKUklO0N5rMBig0Wig1+vhz2ltiJxKSgrwxhtA27bA7t1Aly5KV0RkH43NKs7VTER2s3mzCF0AWLaMoUsEMHiJyE7OnAH+7vqB5GRg9Ghl6yFyFAxeIrKL5GSgsBDo2RN49VWlqyFyHAxeImp2n30mNk9PMXSoZUulKyJyHAxeImpWx48DTz0l9mfOBKKjla2HyNEweImo2ZjNwCOPAGfPAoMGAc89p3RFRI6HwUtEzea990RPZl9f0cTs5aV0RUSOh8FLRM3i+HExFzMAzJkDXHONsvUQOSoGLxFdNUkCnngCKCsDBg+uWmuXiGpi8BLRVVu5EtiwAfD2Fkv9cRp2oroxeInoqpSUAE8/LfZnzgT69FG2HiJHx+AloqsydSpQWgr07w9Mn650NUSOj8FLRE32zTfAihWAh4doYvb2VroiIsfH4CWiJjl3DnjySbH/r38BUVHK1kPkLBi8RNQkL7wghhCFhYl9ImocBi8R2eyPP4CMDLGfmcm5mIlsweAlIpuYzaKJ2WQC/vEP4LbblK6IyLkweInIJh9+CGzdCrRuXXXVS0SNx+AlokYrLQWmTRP7L74IdO6sbD1EzojBS0SNNmMGcPq0GLNrmTSDiGzD4CWiRvntNzFWFwAWLwZatFC2HiJnxeAlogZdulS1uP2jjwJDhihbD5EzY/ASUYPee08MIWrXDpg7V+lqiJxbk4I3MzMToaGh8PHxQUxMDLZv317v+WfPnkVycjI6duwItVqNnj17YuPGjU0qmIjkdeaMWPwAEB2q2rdXth4iZ2fzXZpVq1YhJSUFS5YsQUxMDDIyMhAfH49Dhw4hMDCwxvkVFRW49dZbERgYiNWrV6NTp044duwY2rRp0xz1E5GdvfQScOqUWHXoiSeUrobI+akkSZJseUJMTAwGDRqERYsWAQDMZjO0Wi0mT56MGTNm1Dh/yZIleO2113Dw4EF4eXk1qUiDwQCNRgO9Xg9/f/8mvQYR2e7gQaBfP3GP97vvgFtvVboiIsfV2Kyyqam5oqICOTk5iIuLq3oBDw/ExcUhOzu71uesX78esbGxSE5ORlBQEPr27Ys5c+bAZDLV+T5GoxEGg6HaRkTy+9e/ROiOHs3QJWouNgVvaWkpTCYTgoKCqh0PCgqCTqer9TlHjhzB6tWrYTKZsHHjRjz//PNYsGABXn755TrfJz09HRqNxrpptVpbyiSiZrBpE7BxI+DlBSxYoHQ1RK7D7r2azWYzAgMD8e677yIyMhIJCQl47rnnsGTJkjqfk5qaCr1eb90KCgrsXSYRXaayEnjmGbH/9NNAeLiy9RC5Eps6VwUEBMDT0xPFxcXVjhcXFyM4OLjW53Ts2BFeXl7w9PS0Huvduzd0Oh0qKirgXcvK2Wq1Gmq12pbSiKgZLV4s7u926AA8/7zS1RC5FpuueL29vREZGYmsrCzrMbPZjKysLMTGxtb6nKFDhyI3Nxdms9l67PDhw+jYsWOtoUtEyiotBdLSxP7LLwMajbL1ELkam5uaU1JSsHTpUixbtgwHDhzAk08+ifLyciQlJQEAxo0bh9TUVOv5Tz75JE6fPo0pU6bg8OHD2LBhA+bMmYPk5OTm+ymIqNmkpQFnzwIDBgATJihdDZHrsXkcb0JCAkpKSjBr1izodDpERERg06ZN1g5X+fn58PCoynOtVotvv/0WzzzzDPr3749OnTphypQpmD59evP9FETULPbuBSzdLzIygMvuEBFRM7F5HK8SOI6XyP4kCRgxAvj+e+Cee4Avv1S6IiLnYpdxvETkur7+WoSuWg289prS1RC5LgYvEcFoFJNlAEBKCtCtm7L1ELkyBi8R4a23gNxcIDgYuKxvJBHZAYOXyM0VFwOzZ4v99HTAz0/ZeohcHYOXyM3NnAmUlQFRUcC4cUpXQ+T6GLxEbmzXLuD998V+RgbgwX8RiOyO/5sRuSlJAqZOFY/33w8MHap0RUTugcFL5Ka+/BL4+WfA1xeYN0/paojcB4OXyA1duAD85z9i/z//Abp0UbYeInfC4CVyQ6+/DuTlAZ07A9OmKV0NkXth8BK5maIiMWwIEE3MrVopWw+Ru2HwErmZ1FSgvByIjQUeeEDpaojcD4OXyI1s3w58/LHYf/NNQKVSth4id8TgJXITluFDgJgoY9AgRcshclsMXiI38dlnQHa2uKdrucdLRPJj8BK5gfJyYPp0sZ+aCoSEKFsPkTtj8BK5gVdfBY4fB7p2Fcv+EZFyGLxELi4/XwQvAMyfL2aqIiLlMHiJXNy0acDFi8CNNwL/+IfS1RARg5fIhf3yC7BqlRg2xOFDRI6BwUvkokwmYMoUsT9xIhARoWg5RPQ3Bi+Ri/rgA7HerkYDvPyy0tUQkQWDl8gFnT0LPPec2H/hBaBDByWrIaLLMXiJXNDs2UBJCdCrF5CcrHQ1RHS5JgVvZmYmQkND4ePjg5iYGGzfvr1Rz1u5ciVUKhXGjBnTlLclokY4eBB46y2xn5EBeHkpWg4RXcHm4F21ahVSUlKQlpaGnTt3YsCAAYiPj8fJkyfrfV5eXh7+/e9/44YbbmhysUTUsJQU4NIl4I47gPh4pashoivZHLyvv/46Jk6ciKSkJPTp0wdLlixBy5Yt8cEHH9T5HJPJhIceeggvvvgiunXr1uB7GI1GGAyGahsRNWzDBuC//xVXua+/rnQ1RFQbm4K3oqICOTk5iIuLq3oBDw/ExcUhOzu7zue99NJLCAwMxIQJExr1Punp6dBoNNZNq9XaUiaRW6qoAJ55RuxPnQqEhytaDhHVwabgLS0thclkQlBQULXjQUFB0Ol0tT7n119/xfvvv4+lS5c2+n1SU1Oh1+utW0FBgS1lErmlhQuBP/8EgoKAmTOVroaI6tLCni9eVlaGsWPHYunSpQgICGj089RqNdRqtR0rI3ItJ04AL74o9tPTAX9/ZeshorrZFLwBAQHw9PREcXFxtePFxcUIDg6ucf5ff/2FvLw8jB492nrMbDaLN27RAocOHUL37t2bUjcRXeY//wHKyoDoaCAxUelqiKg+NjU1e3t7IzIyEllZWdZjZrMZWVlZiI2NrXF+r169sGfPHuzevdu63XnnnRg+fDh2797Ne7dEzWDLFuDTT8U8zG+/DXhwdD6RQ7O5qTklJQWJiYmIiopCdHQ0MjIyUF5ejqSkJADAuHHj0KlTJ6Snp8PHxwd9+/at9vw2bdoAQI3jRGS7ysqqCTKeeAKIjFS2HiJqmM3Bm5CQgJKSEsyaNQs6nQ4RERHYtGmTtcNVfn4+PPgnN5Es3nwT2L8fCAgAXnlF6WqIqDFUkiRJShfREIPBAI1GA71eD3/2GiECABw/LqaELC8XCyL83ehERAppbFbx0pTISf3rXyJ0hwxhhyoiZ8LgJXJC338PfP656EiVmckOVUTOhP+7EjkZoxGYNEnsT5rEBe6JnA2Dl8jJzJkDHDokZqh66SWlqyEiWzF4iZzIvn1iZipATBGp0ShbDxHZjsFL5CTMZuCxx8TY3dGjgX/+U+mKiKgpGLxETmLJEmDrVqB1a9GhSqVSuiIiagoGL5ETOH4cmDFD7KenA5xtlch5MXiJHJwkid7LZWXA4MHAk08qXRERXQ0GL5GD++orYN06wMsLWLoU8PRUuiIiuhoMXiIHVloKPPWU2J8+HeDaIkTOj8FL5MCeego4eRK49lpg5kylqyGi5sDgJXJQq1YBX3wBtGgBLFsGqNVKV0REzYHBS+SAdLqqJubnnuM6u0SuhMFL5GAkSUyUcfo0cN11IniJyHUweIkczMcfA19/LXoxL1smHonIdTB4iRzI0aPA00+L/RdfBPr1U7YeImp+DF4iB1FZCTz4IGAwALGxwH/+o3RFRGQPDF4iB/Hii8C2bWLFoRUrRG9mInI9DF4iB7Bli1hnFwDeeQcIDVWyGiKyJwYvkcJOnQIeflj0Zn7kESAhQemKiMieGLxECjKbRdgWFgI9ewJvvaV0RURkbwxeIgW9+iqwfj3g7Q189hnQqpXSFRGRvTUpeDMzMxEaGgofHx/ExMRg+/btdZ67dOlS3HDDDWjbti3atm2LuLi4es8nchdZWVWTY7z1FjBwoLL1EJE8bA7eVatWISUlBWlpadi5cycGDBiA+Ph4nDx5stbzt2zZggceeAA//vgjsrOzodVqMWLECBQWFl518UTO6vhx4IEHRFPz+PFipioicg8qSZIkW54QExODQYMGYdGiRQAAs9kMrVaLyZMnY8aMGQ0+32QyoW3btli0aBHGjRvXqPc0GAzQaDTQ6/Xw9/e3pVwih1NRAdx0kxg6FBEBbN0K+PoqXRURXa3GZpVNV7wVFRXIyclBXFxc1Qt4eCAuLg7Z2dmNeo3z58+jsrIS7dq1q/Mco9EIg8FQbSNyBZIEPPmkCN02bYAvv2ToErkbm4K3tLQUJpMJQUFB1Y4HBQVBp9M16jWmT5+OkJCQauF9pfT0dGg0Guum1WptKZPIYb3+OvDBB4CHh5gko1s3pSsiIrnJ2qt57ty5WLlyJdasWQMfH586z0tNTYVer7duBQUFMlZJZB9ff101DeTrrwO33aZsPUSkDJsmpQsICICnpyeKi4urHS8uLkZwcHC9z50/fz7mzp2L77//Hv3796/3XLVaDTVX/SYX8scfYh5mSQIef7xqIQQicj82XfF6e3sjMjISWVlZ1mNmsxlZWVmIjY2t83mvvvoqZs+ejU2bNiEqKqrp1RI5oYICYNQo4Nw54OabgYULAZVK6aqISCk2T8OekpKCxMREREVFITo6GhkZGSgvL0dSUhIAYNy4cejUqRPS09MBAPPmzcOsWbOwYsUKhIaGWu8Ft27dGq1bt27GH4XI8Zw6BYwYIYYP9eoFfPEF19clcnc2B29CQgJKSkowa9Ys6HQ6REREYNOmTdYOV/n5+fDwqLqQXrx4MSoqKvDPf/6z2uukpaXhhRdeuLrqiRxYebm40j14EOjcGfj2W6CezvxE5CZsHserBI7jJWdTUQHcdRewaRPQti3w669Anz5KV0VE9mSXcbxE1LCKCuD++0Xo+voCGzYwdImoCoOXqBlZQnfNGkCtFo/19DskIjfE4CVqJleG7tq1QHy80lURkaNh8BI1gwsXgHvvrR66I0cqXRUROSKbezUTUXVnzgB33ik6UDF0iaghDF6iq1BYKEJ2715AoxGL2t94o9JVEZEjY/ASNdHevWKcbn4+0LGj6MXcwGyoRES8x0vUFOvWid7K+flAz55iTV2GLhE1BoOXyAaSBLz8MjBmTNXcy1u3AqGhSldGRM6CTc1EjVRaCiQlAd98I76ePBlYsIBzLxORbRi8RI2wZQvw0ENAUZHoubxoEfDoo0pXRUTOiE3NRPUwGoGZM0WTclERcM01wP/9H0OXiJqOV7xEdcjOBiZMAA4cEF8/8gjw1ltAq1bK1kVEzo1XvERXKCsDpk4Fhg4VoRsYCHz+OfD++wxdIrp6DF6iv5lMIlzDw4E33xQ9mMeNA/bvF9NBEhE1BzY1k9uTJOCHH4B//xvYvVsc69EDWLiQUz8SUfPjFS+5LUkCvv9eTPEYFydCV6MBXn8d2LePoUtE9sErXnI7ly6JmacWLBAdqAAxROixx4BZs4CAAGXrIyLXxuAlt1FSArz3HrB4MVBQII75+ACPPw5MmwaEhChbHxG5BwYvubQLF4CvvwY++UQsYnDpkjjeoYO4wp00CQgOVrZGInIvDF5yOXo98O23InDXrwcMhqrvDRokwva++8TVLhGR3Bi85PQqK4GdO8W0jps3Az/9VHVlCwBdugAPPyy23r0VK5OICACDl5yMJAEnToig3bkT+O03sZWXVz/vmmuA0aOBO+8UE2F4sP8+ETkIBi85JLMZKCwE/vwTOHxYbAcOALt2AcXFNc9v21YMCxo2DLj9drFGLhGRI2pS8GZmZuK1116DTqfDgAEDsHDhQkRHR9d5/hdffIHnn38eeXl5CA8Px7x583D77bc3uWhyXpcuAWfPAqdPi624WATslVtenugYVRsPD6BPH2DgQCAqCrjpJqBvX17VEpFzsDl4V61ahZSUFCxZsgQxMTHIyMhAfHw8Dh06hMDAwBrnb926FQ888ADS09Nxxx13YMWKFRgzZgx27tyJvn37NssPYYuLF0VzpSSJry2Pl+/besze58vxnmazuFd66VLtj3V978IF4Px50dRb2+P586JzkyVo9Xo0WosWQLdu4uo1PFw8Xncd0K8f0LJl41+HiMiRqCTp8n9+GxYTE4NBgwZh0aJFAACz2QytVovJkydjxowZNc5PSEhAeXk5vrGsHg5g8ODBiIiIwJIlS2p9D6PRCKPRaP3aYDBAq9VCr9fD39/flnJrCAgATp26qpegZuDvD7RrJ/57dOpUfevcGejaFQgNFeFLROQMDAYDNBpNg1ll0z9rFRUVyMnJQWpqqvWYh4cH4uLikG2ZAugK2dnZSElJqXYsPj4ea9eurfN90tPT8eKLL9pSmtNSqao/KnVMpQK8vETQeXlV36/v0ddXXH22alX3Y+vWQPv2ImjbtQPatBHPJyJyRzYFb2lpKUwmE4KCgqodDwoKwsGDB2t9jk6nq/V8nU5X5/ukpqZWC2vLFW9zyMur2lcq7IiIyH05ZEOeWq2GWq22y2u3bm2XlyUiImoUm/qBBgQEwNPTE8VXjOcoLi5GcB3z7gUHB9t0PhERkSuzKXi9vb0RGRmJrKws6zGz2YysrCzExsbW+pzY2Nhq5wPA5s2b6zyfiIjIldnc1JySkoLExERERUUhOjoaGRkZKC8vR1JSEgBg3Lhx6NSpE9LT0wEAU6ZMwU033YQFCxZg1KhRWLlyJXbs2IF33323eX8SIiIiJ2Bz8CYkJKCkpASzZs2CTqdDREQENm3aZO1AlZ+fD4/LZjIYMmQIVqxYgZkzZ+LZZ59FeHg41q5dq8gYXiIiIqXZPI5XCY0dG0VERKQUu4zjVYrlbwPD5eu7ERERORBLRjV0PesUwVtWVgYAzTaWl4iIyF7Kysqg0Wjq/L5TNDWbzWYUFRXBz88PKheehcIyUUhBQQGb1G3Az812/Myahp9b07jL5yZJEsrKyhASElKtr9OVnOKK18PDA507d1a6DNn4+/u79C+nvfBzsx0/s6bh59Y07vC51Xela8GF1IiIiGTE4CUiIpIRg9eBqNVqpKWl2W2ealfFz812/Myahp9b0/Bzq84pOlcRERG5Cl7xEhERyYjBS0REJCMGLxERkYwYvERERDJi8Do4o9GIiIgIqFQq7N69W+lyHFpeXh4mTJiAsLAw+Pr6onv37khLS0NFRYXSpTmczMxMhIaGwsfHBzExMdi+fbvSJTm09PR0DBo0CH5+fggMDMSYMWNw6NAhpctyKnPnzoVKpcLUqVOVLkVxDF4HN23aNISEhChdhlM4ePAgzGYz3nnnHezbtw9vvPEGlixZgmeffVbp0hzKqlWrkJKSgrS0NOzcuRMDBgxAfHw8Tp48qXRpDuunn35CcnIytm3bhs2bN6OyshIjRoxAeXm50qU5hd9//x3vvPMO+vfvr3QpjkEih7Vx40apV69e0r59+yQA0q5du5Quyem8+uqrUlhYmNJlOJTo6GgpOTnZ+rXJZJJCQkKk9PR0BatyLidPnpQASD/99JPSpTi8srIyKTw8XNq8ebN00003SVOmTFG6JMXxitdBFRcXY+LEifjkk0/QsmVLpctxWnq9Hu3atVO6DIdRUVGBnJwcxMXFWY95eHggLi4O2dnZClbmXPR6PQDwd6sRkpOTMWrUqGq/c+7OKRZJcDeSJGH8+PF44oknEBUVhby8PKVLckq5ublYuHAh5s+fr3QpDqO0tBQmkwlBQUHVjgcFBeHgwYMKVeVczGYzpk6diqFDh6Jv375Kl+PQVq5ciZ07d+L3339XuhSHwiteGc2YMQMqlare7eDBg1i4cCHKysqQmpqqdMkOobGf2+UKCwsxcuRI3HvvvZg4caJClZMrSk5Oxt69e7Fy5UqlS3FoBQUFmDJlCj799FP4+PgoXY5D4ZSRMiopKcGpU6fqPadbt26477778PXXX1dbe9hkMsHT0xMPPfQQli1bZu9SHUpjPzdvb28AQFFREYYNG4bBgwfjo48+qnddTHdTUVGBli1bYvXq1RgzZoz1eGJiIs6ePYt169YpV5wTmDRpEtatW4eff/4ZYWFhSpfj0NauXYu7774bnp6e1mMmkwkqlQoeHh4wGo3VvudOGLwOKD8/HwaDwfp1UVER4uPjsXr1asTExLjV2sS2KiwsxPDhwxEZGYnly5e77f/Y9YmJiUF0dDQWLlwIQDSddunSBZMmTcKMGTMUrs4xSZKEyZMnY82aNdiyZQvCw8OVLsnhlZWV4dixY9WOJSUloVevXpg+fbpbN9PzHq8D6tKlS7WvW7duDQDo3r07Q7cehYWFGDZsGLp27Yr58+ejpKTE+r3g4GAFK3MsKSkpSExMRFRUFKKjo5GRkYHy8nIkJSUpXZrDSk5OxooVK7Bu3Tr4+flBp9MBEIue+/r6KlydY/Lz86sRrq1atUL79u3dOnQBBi+5kM2bNyM3Nxe5ubk1/kBhw06VhIQElJSUYNasWdDpdIiIiMCmTZtqdLiiKosXLwYADBs2rNrxDz/8EOPHj5e/IHJqbGomIiKSEXudEBERyYjBS0REJCMGLxERkYwYvERERDJi8BIREcmIwUtERCQjBi8REZGMGLxEREQyYvASERHJiMFLREQkIwYvERGRjBi8REREMmLwEhERyYjBS0REJCMGLxERkYwYvERERDJqoXQBjWE2m1FUVAQ/Pz+oVCqlyyEiIqpBkiSUlZUhJCQEHh51X9c6RfAWFRVBq9UqXQYREVGDCgoK0Llz5zq/7xTB6+fnB0D8MP7+/gpXQ0REVJPBYIBWq7VmVl2cIngtzcv+/v4MXiIicmgN3RJl5yoiIiIZMXiJiIhkxOAlIiKSEYOXiIhIRgxeIiJyS4WGQpSeL4XJbJL1fRm8RETklvov6Y8Or3XAoVOHZH1fBi8REbml8opyAEBr79ayvi+Dl4iI3M4l8yUYTUYAQCuvVrK+N4OXiIjcjuVqFwBaeTN4iYiI7Kq8UgSvh8oDak+1rO/N4CUiIrdz+f1duVe9Y/ASEZHbOVdxDoD893cBBi8REbkhS1Oz3Pd3AQYvERG5IaWGEgEMXiIickNsaiYiIpIRm5qJiIhkZGlq5hUvERGRDCxXvLzHS0REJAPe4yUiIpKRtamZ93iJiIjsj03NREREMmJTMxERkYw4nIiIiEhGHE5EREQkI0tTM+/xEhERycDlm5oLCwvx8MMPo3379vD19UW/fv2wY8cOOd6aiIioBiWbmlvY+w3OnDmDoUOHYvjw4fjvf/+LDh064M8//0Tbtm3t/dZERES1UnI4kd2Dd968edBqtfjwww+tx8LCwup9jtFohNFotH5tMBjsVh8REbkf63AiV2xqXr9+PaKionDvvfciMDAQ1113HZYuXVrvc9LT06HRaKybVqu1d5lEROQmJEly7V7NR44cweLFixEeHo5vv/0WTz75JJ5++mksW7aszuekpqZCr9dbt4KCAnuXSUREbqLCVAGTZALgok3NZrMZUVFRmDNnDgDguuuuw969e7FkyRIkJibW+hy1Wg21Wm3v0oiIyA1ZmpkBF21q7tixI/r06VPtWO/evZGfn2/vtyYiIqrB0rHK29MbLTzsfv1Zg92Dd+jQoTh06FC1Y4cPH0bXrl3t/dZEREQ1KHl/F5AheJ955hls27YNc+bMQW5uLlasWIF3330XycnJ9n5rIiKiGpQcSgTIELyDBg3CmjVr8Nlnn6Fv376YPXs2MjIy8NBDD9n7rYmIiGpQcigRIEPnKgC44447cMcdd8jxVkRERPVy+aZmIiIiR+LyTc1ERESOROmmZgYvERG5FTY1ExERyUjJJQEBBi8REbkZyxVvay/e4yUiIrI73uMlIiKSkbWpmfd4iYiI7I/DiYiIiGTEpmYiIiIZcTgRERGRjDiciIiISEbW4US8x0tERGR/1nu8bGomIiKyPzY1ExERyYhNzURERDIxS2ZOoEFERCSXC5UXrPtsaiYiIrIzy9UuALT0aqlIDQxeIiJyG5b7uy29WsJDpUwEMniJiMhtKD2UCGDwEhGRG1F6KBHA4CUiIjei9FAigMFLRERuhE3NREREMmJTMxERkYyUXhIQUCB4586dC5VKhalTp8r91kRE5OYsV7xuc4/3999/xzvvvIP+/fvL+bZEREQA3Owe77lz5/DQQw9h6dKlaNu2bb3nGo1GGAyGahsREdHVsjY1u8M93uTkZIwaNQpxcXENnpueng6NRmPdtFqtDBUSEZGrc5um5pUrV2Lnzp1IT09v1PmpqanQ6/XWraCgwM4VEhGRO3CEpuYW9n6DgoICTJkyBZs3b4aPj0+jnqNWq6FWq+1cGRERuRtHGE5k9+DNycnByZMnMXDgQOsxk8mEn3/+GYsWLYLRaISnp6e9yyAiInKI4UR2D95bbrkFe/bsqXYsKSkJvXr1wvTp0xm6REQkG0e4x2v34PXz80Pfvn2rHWvVqhXat29f4zgREZE9We/xukOvZiIiIqW5RVNzbbZs2aLE2xIRkZtzhKZmXvESEZHbYFMzERGRjByhqZnBS0REbsFkNsFoMgJgUzMREZHdWe7vAmxqJiIisjvL/V0PlQfUnsrNjsjgJSIit3D5/V2VSqVYHQxeIiJyC44wlAhg8BIRkZtwhKFEAIOXiIjchCMMJQIYvERE5CbY1ExERCQj6xUvm5qJiIjsz3qPl03NRERE9mdpauYVLxERkQwsTc2tvXiPl4iIyO44nIiIiEhG1qZm3uMlIiKyPw4nIiIikhGHExEREcmIw4mIiIhkxOFEREREMrIOJ+I9XiIiIvvSX9TjuOE4ADY1ExER2ZVZMuOhrx5CyfkSdPbvjMiQSEXrYfASEZFLm/XjLGz4cwN8WvhgbcJatPRqqWg9dg/e9PR0DBo0CH5+fggMDMSYMWNw6NAhe78tERERVu9fjVd+eQUAsHT0UsWvdgEZgvenn35CcnIytm3bhs2bN6OyshIjRoxAeXm5vd+aiIjc2J7iPRi/djwAIGVwCh7u/7CyBf1NJUmSJOcblpSUIDAwED/99BNuvPHGRj3HYDBAo9FAr9fD39/fzhUSEZGz+zb3Wzz41YM4feE0bu12KzY+tBEtPFrY9T0bm1X2raIWer0eANCuXbs6zzEajTAajdavDQaD3esiIiLnZ5bMSP8lHc//+DwkSBgUMggr/7nS7qFrC1k7V5nNZkydOhVDhw5F37596zwvPT0dGo3Gumm1WhmrJCIiZ3T24lncvepuzPxxJiRIeGzgY/gl6Re08637Qk8JsjY1P/nkk/jvf/+LX3/9FZ07d67zvNqueLVaLZuaiYioBrNkxvI/lmPa5mkoLi+G2lONzNszMWHgBFnrcLim5kmTJuGbb77Bzz//XG/oAoBarYZarZapMiIiclY7T+zEpI2TkH08GwAQ3i4cK/6xAlEhUQpXVje7B68kSZg8eTLWrFmDLVu2ICwszN5vSURELm7fyX1I/zUdK/asgAQJrbxa4fkbn8fUwVOhbuHYF252D97k5GSsWLEC69atg5+fH3Q6HQBAo9HA19fX3m9PREQuJKcoB6/88grWHFxjPfZgvwfxatyr6OTfScHKGs/u93hVKlWtxz/88EOMHz++Ua/B4URERO7LeMmIrw58hcU7FuOX/F8AACqocE/ve/DsDc9iYMeBClcoOMw9XpmHCRMRkYs4WHoQH+3+CB/s+gAl50sAAJ4qTzzQ7wGkXp+KPh36KFxh0zjOwCYiInJ7unM6rNy7Esv/WI6cEznW4538OuGxyMcw4boJTtOkXBcGLxERKepQ6SGsP7Qe6w6tw9aCrZAgWkpbeLRAfPd4PDrwUdzR8w6HmgTjarjGT0FERE7DZDZh2/FtWHdoHdYfWo9Dp6ovnBPbORYP938Y9117HwJaBihUpf0weImIyO6Kyorww9Ef8P2R77Hxz43We7YA4OXhheFhw3HXNXdhdM/R0Gpce7ZCBi8RETW70xdOY0veFmQdycIPeT/gYOnBat9v49MGt4ffjruuuQvx3eOh8dEoVKn8GLxERHTVdOd02FqwFb/l/4Ytx7Zg14ld1nu1gBj+M7DjQNwSdgtGdB+BG7veCC9PLwUrVg6Dl4iIbGIym7D35F5sLdiKrcdF2B49e7TGeX069MHNoTfj5rCbMSx0GNr6tlWgWsfD4CUiojpJkoRj+mPYUbQDvxf+jh0nxGNZRVm181RQoV9QPwzpPATXd7keN4fdjI5+HRWq2rExeImICIAI2QJDAXad2IUdRTuw48QO7CjagdLzpTXO9fP2w+DOgzFEOwRDtUMR0zkG/mrOLNgYDF4iIjd08dJF7Du5D/8r/h/+p/sf/lf8P/xR/AfOXDxT41wvDy/0D+qPqJAoDAoZhEGdBuHaDtfC08NTgcqdH4OXiMiFSZKEE+dO4I/iP6wB+7/i/+FQ6SGYJFON81t4tECfDn0Q1TEKUSFi6x/U3+FX/HEmDF4iIhdglswo0BfgQOkB7C/Zj/0l+637Zy+erfU5AS0DMCBogNiCB6B/UH/0DujNkLUzBi8RkRMxmU04cuZItWA9UHoAB0oOoLyyvNbneKg8cE37azAgeEC1oO3YumOdK8iR/TB4iYgc0NmLZ/HnqT/x5+k/8eepP60he/jUYRhNxlqf4+XhhZ7te6JPhz7oHdAbfTr0QZ8OfRDePhw+LXxk/gmoLgxeIiKFnK88j9zTuTh86jD+PPUnDp/++/HU4WpTKl7Jt4UvegX0qhGw3dp2c9tJKZwJg5eIyI4uVF5A3tm8qoA9/af18bjheL3PDW4djPB24ejZvieuaX+NNWC7tukKD5WHTD8BNTcGLxHRVZAkCSfLT+LImSP468xfOHLmiHX768xfKCorqvf5bX3aomf7nujZvqc1ZMPbh6NHux4cF+uiGLxERA0wXjIi72xetUC9PGDr6tRk4efth+7tuouAbSeC1RK07Vu2l+mnIEfB4CUit2cym1BYVoi8s3nIO5uHY2eP4ejZo9ZgPW44Xm3C/yupoIJWo0W3tt3QvW13dGvbrdp+O9927D1MVgxeInJ5l8yXUGioCta8s3nI01eFbIGhAJfMl+p9jVZerdC93d+h2qZb1X7bbuiq6cqxr9RoDF4icnqVpkocNxyvumLVH6sWsscNx2udpelyXh5e6KLpgtA2oQhtE4qumq7iqvXvgO3QsgOvWqlZMHiJyOEZjAbk6/ORr89Hgb5A7BvE15ZgNUvmel/D29MbXTVdqwWrZT+0TSiCWwdz7mGSBYOXiBRVYapAoaFQhKqhoCpgL9s3GA0Nvo7aUy0CtU1XhGpCq4Vq1zZdEdw6mENwyCEweInIbiRJQsn5khpXq5eHqu6crt6OSxbtfNuhi6YLumi6QOuvte5bwjWwVSCDlZwCg5eImuxcxblaw9SyX6AvqHN6w8upPdVVoarRoov/Zft/B20r71Yy/ERE9idb8GZmZuK1116DTqfDgAEDsHDhQkRHR8v19kRko0vmSygqK6p+X/WKgK1t7dYrqaBCR7+ONa5UL98PaBnAjkvkNmQJ3lWrViElJQVLlixBTEwMMjIyEB8fj0OHDiEwMFCOEojoMpIk4fSF0/XeVy0qK2qwwxIAaNSaOq9Uu2i6IMQvBN6e3jL8VETOQSVJUsM3V65STEwMBg0ahEWLFgEAzGYztFotJk+ejBkzZtQ432g0wmisap4yGAzQarXQ6/Xw9+cUakQNuVB5oVpzb20Be77yfIOv4+XhBa1GW+eVqlaj5bSGRH8zGAzQaDQNZpXdr3grKiqQk5OD1NRU6zEPDw/ExcUhOzu71uekp6fjxRdftHdpRE7JZDbhxLkTtYaq5bH0fGmjXiuoVVDV1al/9StVrb8WQa2D2GGJqJnZPXhLS0thMpkQFBRU7XhQUBAOHjxY63NSU1ORkpJi/dpyxUvk6iRJwpmLZ2q9p2p5LDQUNjgZBCBmWrqyCfjyZuDO/p25RiuRAhyyV7NarYZazenXyPVcqLyA44bj9fYCbmjCfQDwVHmis3/nasF6eQ/gLpouaOPThh2WiByQ3YM3ICAAnp6eKC4urna8uLgYwcHB9n57ItmYzCbozulqBKllhqUCfUG9i5tfrkPLDjWC9PJ9zrJE5LzsHrze3t6IjIxEVlYWxowZA0B0rsrKysKkSZPs/fZEzcZ4yWidovCY/hiOnT1mnRM4X5+PwrLCBifaB4CWXi1rBOnl4drZvzN8vXxl+ImISAmyNDWnpKQgMTERUVFRiI6ORkZGBsrLy5GUlCTH2xM1yrmKc9XC1LJv+Vp3Ttfga3iqPNHJv1OtoWq5gm3r05ZNwERuTJbgTUhIQElJCWbNmgWdToeIiAhs2rSpRocrInuRJAlnL56tEaqXX72eunCqwddp6dUSXTVdrfMBd23T1fp1F00XdGzdkU3ARFQvWcbxXq3Gjo0i96a/qLcuXH707NFqoZp3Ng9lFWUNvoZGrbFOqm9ZvcYSrF01XTnDEhHVyWHG8RI1l0pTJfL1+dZgtYSs5evTF043+BodWnaoNVQt+xofjQw/CRG5MwYvOQxJklB6vrTWUD1y5gjy9fkNTmHYoWUHhLUNQ1gbsV0eql00XTjRPhEpjsFLspIkCbpzOuSezsWfp//En6f+xJ+n/0Tu6Vz8deYvnKs4V+/z1Z5qdGvbDWFtw9CtTbeq/bbdENYmDH5qP5l+EiKipmHwUrOTJAnF5cUiXP8OVku45p7ObTBcO/l1sobpleHKxcyJyNkxeKnJyivKcfjUYRwoPYCDpQdx6NQh/HlKBGx9HZk8VB7oqumKHu16ILxdOMLbh6NHux7o3rY7wtqGcRpDInJpDF6qlyRJKDlfggMlIlwtIXug9ADy9fl1Pk8FFbq26YrwduE1AjasTRjULTglKBG5JwYvAQDMkhlHzxzFgdIDNUK2vsXOA1oGoHdAb/QK6IVeAb2sActwJSKqHYPXDZWUl2DPyT3YU7wHfxT/gT0n92Bfyb4612dVQYWwtmHoFdDLGrK9A3rjmoBrENAyQObqiYicG4PXhV28dBH7S/aLcC3egz0nRdAWlxfXer7aUy1CtUNv9Gr/9+PfV7GcO5iIqHkweF3EhcoL+KP4D+ScyMGOoh3IOZGDfSf31bpuqwoqdGvbDf2C+qFfoNj6B/VHj3Y9ON0hEZGdMXidkCVkLQFbX8i2922P/kH9RcD+HbTXBl6L1t6tFaiciIgYvA5OkiT8efpPbC3Yit/yf8P2ou11hmxgq0BEdoxEZMdIRIVEITIkEp38OnFuYSIiB8LgdTAXKi9gR9EOEbQFv2FrwdZaV82xhGxUSJQIW4YsEZFTYPAqzHjJiG3HtyHraBZ+OPoDthduR6W5sto5Pi18MChkEIZoh2Bw58GIColiyBIROSkGr8wumS9h54md+OHoD8g6moVf83/FxUsXq53TsXVHDO0yFEM6D8EQ7RBc1/E6eHt6K1QxERE1JwavDM5cOIP/5v4X6w6tw7e530Jv1Ff7flCrINwcdjNuCbsFw8OGI6xNGK9miYhcFIPXTo6eOYr1h9Zj/eH1+PnYz7hkvmT9nkatwbDQYbgl7BbcHHYz+nTow6AlInITDN5mtL9kP1buXYm1B9diz8k91b7Xp0Mf3HXNXRjdczSiO0VzvCwRkZti8F6lE2UnsHLvSizfsxw7T+y0HvdQeeD6Ltfjrmvuwp3X3Ike7XooWCURETkKBm8TmCUzvj/yPRbvWIyvD31tHVPbwqMFRvYYiXv73ItR4aPQvmV7hSslIiJHw+C1gcFowNKcpViSswS5p3Otxwd3Hoyx/cfivmvv46IBRERULwZvI5y+cBpv/d9bePP/3sTZi2cBAP5qfyQOSMQTUU+gT4c+yhZIREROg8FbD4PRgDm/zEHm75k4V3EOANAroBf+FfsvPND3AbTybqVwhURE5GwYvLUwS2Ys/2M5pm2eZl1Cb0DQADx3w3O4p/c97JFMRERN5mHPF8/Ly8OECRMQFhYGX19fdO/eHWlpaaioqLDn216VXSd24foPrkfi2kQUlxejZ/ueWH//eux6fBfuvfZehi4REV0Vu17xHjx4EGazGe+88w569OiBvXv3YuLEiSgvL8f8+fPt+dY2kyQJi7YvQsp3KbhkvoRWXq0w66ZZmDp4KqdrJCKiZqOSJEmS8w1fe+01LF68GEeOHGn0cwwGAzQaDfR6Pfz9/Zu9pvOV5/HY14/h0z2fAgDu6X0P3hr5Fjr5d2r29yIiItfU2KyS/R6vXq9Hu3bt6j3HaDTCaDRavzYYDHar56/Tf+Gez+/BH8V/wFPlifkj5mNKzBRO4UhERHZh13u8V8rNzcXChQvx+OOP13teeno6NBqNddNqtXapJ1+fjyEfDMEfxX8gsFUgssZlYergqQxdIiKymyYF74wZM6BSqerdDh48WO05hYWFGDlyJO69915MnDix3tdPTU2FXq+3bgUFBU0ps17nK89jzMoxOFl+Ev2D+mPnYztxU+hNzf4+REREl2vSPd6SkhKcOnWq3nO6desGb2/RKamoqAjDhg3D4MGD8dFHH8HDw7a8b+57vJIk4eE1D2PFnhUIaBmAHRN3oGubrlf9ukRE5L7seo+3Q4cO6NChQ6POLSwsxPDhwxEZGYkPP/zQ5tC1hwXZC7Bizwp4qjyx+t7VDF0iIpKNXTtXFRYWYtiwYejatSvmz5+PkpIS6/eCg4Pt+dZ1+u6v7zD9++kAgIyRGWxeJiIiWdk1eDdv3ozc3Fzk5uaic+fO1b4n8ygmAECBvgD3r74fZsmMRyIeQfKgZNlrICIi92bXdt/x48dDkqRaNyWE+IXgscjHMLjzYLw96m32XiYiItm51VzNnh6emBs3F8ZLRqhbqJUuh4iI3JDyPZ0UwNAlIiKluGXwEhERKYXBS0REJCMGLxERkYwYvERERDJyil7NluFH9lyliIiI6GpYMqqhIbNOEbxlZWUAYLdVioiIiJpLWVkZNBpNnd9v0iIJcjObzSgqKoKfn5/Nk14YDAZotVoUFBQ0ywIL7oSfXdPwc2safm5Nx8+uaZr7c5MkCWVlZQgJCal3XQKnuOL18PCoMeWkrfz9/fkL2UT87JqGn1vT8HNrOn52TdOcn1t9V7oW7FxFREQkIwYvERGRjFw+eNVqNdLS0qBWc5pIW/Gzaxp+bk3Dz63p+Nk1jVKfm1N0riIiInIVLn/FS0RE5EgYvERERDJi8BIREcmIwUtERCQjBi8REZGMXCJ4MzMzERoaCh8fH8TExGD79u31nv/FF1+gV69e8PHxQb9+/bBx40aZKnU8tnx2S5cuxQ033IC2bduibdu2iIuLa/CzdlW2/s5ZrFy5EiqVCmPGjLFvgQ7K1s/t7NmzSE5ORseOHaFWq9GzZ0+3/f/V1s8uIyMD11xzDXx9faHVavHMM8/g4sWLMlXrGH7++WeMHj0aISEhUKlUWLt2bYPP2bJlCwYOHAi1Wo0ePXrgo48+av7CJCe3cuVKydvbW/rggw+kffv2SRMnTpTatGkjFRcX13r+b7/9Jnl6ekqvvvqqtH//fmnmzJmSl5eXtGfPHpkrV56tn92DDz4oZWZmSrt27ZIOHDggjR8/XtJoNNLx48dlrlxZtn5uFkePHpU6deok3XDDDdJdd90lT7EOxNbPzWg0SlFRUdLtt98u/frrr9LRo0elLVu2SLt375a5cuXZ+tl9+umnklqtlj799FPp6NGj0rfffit17NhReuaZZ2SuXFkbN26UnnvuOemrr76SAEhr1qyp9/wjR45ILVu2lFJSUqT9+/dLCxculDw9PaVNmzY1a11OH7zR0dFScnKy9WuTySSFhIRI6enptZ5/3333SaNGjap2LCYmRnr88cftWqcjsvWzu9KlS5ckPz8/admyZfYq0SE15XO7dOmSNGTIEOm9996TEhMT3TJ4bf3cFi9eLHXr1k2qqKiQq0SHZetnl5ycLN18883VjqWkpEhDhw61a52OrDHBO23aNOnaa6+tdiwhIUGKj49v1lqcuqm5oqICOTk5iIuLsx7z8PBAXFwcsrOza31OdnZ2tfMBID4+vs7zXVVTPrsrnT9/HpWVlWjXrp29ynQ4Tf3cXnrpJQQGBmLChAlylOlwmvK5rV+/HrGxsUhOTkZQUBD69u2LOXPmwGQyyVW2Q2jKZzdkyBDk5ORYm6OPHDmCjRs34vbbb5elZmclVz44xepEdSktLYXJZEJQUFC140FBQTh48GCtz9HpdLWer9Pp7FanI2rKZ3el6dOnIyQkpMYvqitryuf266+/4v3338fu3btlqNAxNeVzO3LkCH744Qc89NBD2LhxI3Jzc/HUU0+hsrISaWlpcpTtEJry2T344IMoLS3F9ddfD0mScOnSJTzxxBN49tln5SjZadWVDwaDARcuXICvr2+zvI9TX/GScubOnYuVK1dizZo18PHxUboch1VWVoaxY8di6dKlCAgIULocp2I2mxEYGIh3330XkZGRSEhIwHPPPYclS5YoXZrD27JlC+bMmYO3334bO3fuxFdffYUNGzZg9uzZSpdGcPIr3oCAAHh6eqK4uLja8eLiYgQHB9f6nODgYJvOd1VN+ews5s+fj7lz5+L7779H//797Vmmw7H1c/vrr7+Ql5eH0aNHW4+ZzWYAQIsWLXDo0CF0797dvkU7gKb8vnXs2BFeXl7w9PS0Huvduzd0Oh0qKirg7e1t15odRVM+u+effx5jx47Fo48+CgDo168fysvL8dhjj+G5556rd5F2d1ZXPvj7+zfb1S7g5Fe83t7eiIyMRFZWlvWY2WxGVlYWYmNja31ObGxstfMBYPPmzXWe76qa8tkBwKuvvorZs2dj06ZNiIqKkqNUh2Lr59arVy/s2bMHu3fvtm533nknhg8fjt27d0Or1cpZvmKa8vs2dOhQ5ObmWv9QAYDDhw+jY8eObhO6QNM+u/Pnz9cIV8sfMBLXxamTbPnQrF21FLBy5UpJrVZLH330kbR//37psccek9q0aSPpdDpJkiRp7Nix0owZM6zn//bbb1KLFi2k+fPnSwcOHJDS0tLcejiRLZ/d3LlzJW9vb2n16tXSiRMnrFtZWZlSP4IibP3cruSuvZpt/dzy8/MlPz8/adKkSdKhQ4ekb775RgoMDJRefvllpX4Exdj62aWlpUl+fn7SZ599Jh05ckT67rvvpO7du0v33XefUj+CIsrKyqRdu3ZJu3btkgBIr7/+urRr1y7p2LFjkiRJ0owZM6SxY8daz7cMJ/rPf/4jHThwQMrMzORworosXLhQ6tKli+Tt7S1FR0dL27Zts37vpptukhITE6ud//nnn0s9e/aUvL29pWuvvVbasGGDzBU7Dls+u65du0oAamxpaWnyF64wW3/nLueuwStJtn9uW7dulWJiYiS1Wi1169ZNeuWVV6RLly7JXLVjsOWzq6yslF544QWpe/fuko+Pj6TVaqWnnnpKOnPmjPyFK+jHH3+s9d8sy2eVmJgo3XTTTTWeExERIXl7e0vdunWTPvzww2avi+vxEhERycip7/ESERE5GwYvERGRjBi8REREMmLwEhERyYjBS0REJCMGLxERkYwYvERERDJi8BIREcmIwUtERCQjBi8REZGMGLxEREQy+n8H3pnIDSBzNAAAAABJRU5ErkJggg==","text/plain":["
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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["from scipy.stats import norm\n","from scipy.stats import uniform\n","import matplotlib.pyplot as plt\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","# Define all the probability functions related to this distribution\n","\n","def dnorm(x, mean = 0, std = 1):\n"," result = norm.pdf(x, loc = mean, scale = std)\n"," return result\n","\n","def pnorm(x, mean = 0, std = 1):\n"," result = norm.cdf(x, loc = mean, scale = std)\n"," return result\n","\n","def qnorm(x, mean = 0, std = 1):\n"," result = norm.ppf(x, loc = mean, scale = std)\n"," return result\n","\n","def rnorm(x, mean = 0, std = 1):\n"," result = norm.rvs(x, loc = mean, scale = std)\n"," return result\n","\n","mean = 0\n","std = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dnorm(data, mean = mean, std = std)\n","cdf = pnorm(data, mean = mean, std = std)\n","ppf = qnorm(data, mean = mean, std = std)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()\n","\n","\n","def dunif(x, low = 0, high = 1):\n"," result = uniform.pdf(x, loc = low, scale = (high - low))\n"," return result\n","\n","def punif(x, low = 0, high = 1):\n"," result = uniform.cdf(x, loc = low, scale = (high - low))\n"," return result\n","\n","def qunif(x, low = 0, high = 1):\n"," result = uniform.ppf(x, loc = low, scale = (high - low))\n"," return result\n","\n","def runif(x, low = 0, high = 1):\n"," result = uniform.rvs(x, loc = low, scale = (high - low))\n"," return result\n","\n","low = 0\n","high = 1\n","data = np.arange(-5, 5, 0.01)\n","\n","pmf = dunif(data, low = low, high = high)\n","cdf = punif(data, low = low, high = high)\n","ppf = qunif(data, low = low, high = high)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].plot(data, pmf, \"r-\")\n","axis[1].plot(data, cdf, \"b-\")\n","axis[2].plot(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.4"}},"nbformat":4,"nbformat_minor":5}