From b5fea0e8038189ac5aed54ef6d7440a06fe8a0da Mon Sep 17 00:00:00 2001
From: bitterspice <karlkc@gmail.com>
Date: Thu, 2 May 2019 19:27:04 -0700
Subject: [PATCH] Add files via upload

---
 Week 4.ipynb | 347 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 347 insertions(+)
 create mode 100644 Week 4.ipynb

diff --git a/Week 4.ipynb b/Week 4.ipynb
new file mode 100644
index 0000000..5a3c116
--- /dev/null
+++ b/Week 4.ipynb	
@@ -0,0 +1,347 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "\n",
+    "_You are currently looking at **version 1.0** of this notebook. To download notebooks and datafiles, as well as get help on Jupyter notebooks in the Coursera platform, visit the [Jupyter Notebook FAQ](https://www.coursera.org/learn/python-data-analysis/resources/0dhYG) course resource._\n",
+    "\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Distributions in Pandas"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "np.random.binomial(1, 0.5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "np.random.binomial(1000, 0.5)/1000"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "chance_of_tornado = 0.01/100\n",
+    "np.random.binomial(100000, chance_of_tornado)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "chance_of_tornado = 0.01\n",
+    "\n",
+    "tornado_events = np.random.binomial(1, chance_of_tornado, 1000000)\n",
+    "    \n",
+    "two_days_in_a_row = 0\n",
+    "for j in range(1,len(tornado_events)-1):\n",
+    "    if tornado_events[j]==1 and tornado_events[j-1]==1:\n",
+    "        two_days_in_a_row+=1\n",
+    "\n",
+    "print('{} tornadoes back to back in {} years'.format(two_days_in_a_row, 1000000/365))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "np.random.uniform(0, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "np.random.normal(0.75)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Formula for standard deviation\n",
+    "$$\\sqrt{\\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{x})^2}$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "distribution = np.random.normal(0.75,size=1000)\n",
+    "\n",
+    "np.sqrt(np.sum((np.mean(distribution)-distribution)**2)/len(distribution))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "np.std(distribution)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import scipy.stats as stats\n",
+    "stats.kurtosis(distribution)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "stats.skew(distribution)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "chi_squared_df2 = np.random.chisquare(2, size=10000)\n",
+    "stats.skew(chi_squared_df2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "chi_squared_df5 = np.random.chisquare(5, size=10000)\n",
+    "stats.skew(chi_squared_df5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "output = plt.hist([chi_squared_df2,chi_squared_df5], bins=50, histtype='step', \n",
+    "                  label=['2 degrees of freedom','5 degrees of freedom'])\n",
+    "plt.legend(loc='upper right')\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Hypothesis Testing"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "df = pd.read_csv('grades.csv')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "len(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "early = df[df['assignment1_submission'] <= '2015-12-31']\n",
+    "late = df[df['assignment1_submission'] > '2015-12-31']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "early.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "late.mean()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from scipy import stats\n",
+    "stats.ttest_ind?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "stats.ttest_ind(early['assignment1_grade'], late['assignment1_grade'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "stats.ttest_ind(early['assignment2_grade'], late['assignment2_grade'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "stats.ttest_ind(early['assignment3_grade'], late['assignment3_grade'])"
+   ]
+  }
+ ],
+ "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": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}