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SW12_Theorie_EN
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{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SW12 - Flipped Classroom \n", "\n", "*This JupyterNotebook is intended to practice the theory alongside the slides and is used as a \"practical check of the theory input\". There are no sample solutions and the file will not be corrected and does not have to be submitted.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "\n", "## Chapter 2.9 - Cumulative distribution function \n", "\n", "\n", "### Example 2.9.1 \n", "\n", "Random variable X and Jass cards" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[<matplotlib.lines.Line2D at 0x1bb0cc7b440>]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "values_jass=[-1,0,2,3,4,10,11,12]\n", "prob_jass=np.array([0,4/9,1/9,1/9,1/9,1/9,1/9,0])\n", "cum_jass=np.cumsum(prob_jass)\n", "plt.step(values_jass,cum_jass, where='post')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "\n", "# Chapter 2.10 - Binomial distribution \n", "\n", "### Comments 2.10.1 " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.3125\n" ] } ], "source": [ "import math\n", "n=5\n", "p=0.5\n", "x=3\n", "print(math.comb(n,x)*p**x*(1-p)**(n-x))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.31249999999999983\n" ] } ], "source": [ "import numpy as np\n", "from scipy.stats import binom\n", "print(binom.pmf(k=3, n=5, p=.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "\n", "### Note 2.10.2 \n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.03125 0.15625 0.3125 0.3125 0.15625 0.03125]\n" ] } ], "source": [ "n, p = 5, 0.5\n", "ran = np.arange(n+1)\n", "print(binom.pmf(ran, n, p))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "\n", "### Example 2.10.2 " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.03125 0.15625 0.3125 0.3125 0.15625 0.03125]\n" ] } ], "source": [ "n, p = 5, 0.5\n", "ran = np.arange(n+1)\n", "print(binom.pmf(ran, n, p))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.03125, 0.15625, 0.3125 , 0.3125 , 0.15625, 0.03125])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "binom.pmf(ran, n, p)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from scipy.stats import binom\n", "import numpy as np\n", "\n", "n,p=10,0.3\n", "x=np.arange(n+1)\n", "y=binom.pmf(x,n,p)\n", "\n", "plt.vlines(x, 0, y, 'g')\n", "plt.plot(x, y, 'go')\n", "plt.xlabel('Number of wins')\n", "plt.ylabel('Probability')\n", "\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", " \n", "### Example 2.10.4 \n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.stats import binom\n", "n, p = 100, 0.5\n", "x = np.arange(n+1)\n", "y = binom.cdf(x, n, p)\n", "plt.step(x, y, 'g', where='post')\n", "plt.plot(x, y, 'go')\n", "plt.xlabel('x')\n", "plt.ylabel('F(x)')\n", "plt.title('Cumulative Distribution Function of Binom(100,0.5)')\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Note 2.10.3 " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5397946186935895" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import binom\n", "binom.cdf(k=50, n=100, p=.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "\n", "end " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 4 }
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