diff --git a/notebook/solutions.ipynb b/notebook/solutions.ipynb index 0bfa8763..2c418a32 100644 --- a/notebook/solutions.ipynb +++ b/notebook/solutions.ipynb @@ -1 +1,222 @@ -{"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","# Uniform\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", + "cumulative_prob = np.linspace(0, 1, len(data))\n", + "ppf = qnorm(cumulative_prob, 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(cumulative_prob, 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", + "# Uniform\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": { + "kernelspec": { + "display_name": "Python 3", + "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 +}