{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 05 Variance and standard deviation of a discrete random variable" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from pandas import Series, DataFrame\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "from scipy import stats, special" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[khanacademy](https://www.khanacademy.org/math/ap-statistics/random-variables-ap/discrete-random-variables/v/variance-and-standard-deviation-of-a-discrete-random-variable?modal=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Variance and standard deviation of a discrete random variable fig 1](./imgs/09-05-01.png)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "df = DataFrame({'x': [0, 1, 2, 3, 4] ,'P(x)': [0.1, 0.15, 0.4, 0.25, 0.1]})" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " x P(x)\n", "0 0 0.10\n", "1 1 0.15\n", "2 2 0.40\n", "3 3 0.25\n", "4 4 0.10" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "mean = np.sum(df['x'] * df['P(x)'])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# caution Linear algebra \n", "mean = np.dot(df['x'], df['P(x)'])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [], "source": [ "var = np.sum((df['x'] - mean)**2 * df['P(x)'])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "std = np.sqrt(var)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.1" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean" ] }, { "cell_type": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.bar(df['x'], df['P(x)'])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.barplot(df['x'], df['P(x)'])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# scipy.norm.mean; scipy.norm.var; scipy.norm.std but how?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 4 }