diff --git a/notebook/problems.ipynb b/notebook/problems.ipynb
index c1fa790d..540d9306 100644
--- a/notebook/problems.ipynb
+++ b/notebook/problems.ipynb
@@ -1 +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":["<Figure size 500x700 with 3 Axes>"]},"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":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":["<Figure size 500x700 with 3 Axes>"]},"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":"markdown","id":"d9ee196e","metadata":{},"source":["**Normal distribution**"]},{"cell_type":"code","execution_count":6,"id":"98d5f012","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 1000x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["from scipy.stats import norm\n","import matplotlib.pyplot as plt\n","import numpy as np\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 = x, loc = mean, scale = std)\n","    return result\n","\n","def qnorm(p, mean = 0, std = 1):\n","    result = norm.ppf(q = p, loc = mean, scale = std)\n","    return result\n","\n","def rnorm(n, mean = 0, std = 1):\n","    result = norm.rvs(size = n, loc = mean, scale = std)\n","    return result\n","\n","np.random.seed(69)\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 = (10, 7))\n","\n","axis[0].plot(data, pmf)\n","axis[1].plot(data, cdf)\n","axis[2].plot(data, ppf)\n","\n","plt.tight_layout()\n","plt.show()"]},{"cell_type":"markdown","id":"b1b278f3","metadata":{},"source":["**Uniform distribution**"]},{"cell_type":"code","execution_count":5,"id":"3b4c3d8a","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 1000x700 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["from scipy.stats import uniform\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","np.random.seed(40)\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 = (10, 7))\n","\n","axis[0].plot(data, pmf)\n","axis[1].plot(data, cdf)\n","axis[2].plot(data, ppf)\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":"3.12.1"}},"nbformat":4,"nbformat_minor":5}