Code/chapter_5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9999\n",
      "   means\n",
      "0    9.0\n",
      "1    5.0\n",
      "2    6.0\n",
      "3    4.5\n",
      "4    4.0\n",
      "         means\n",
      "9994  4.998799\n",
      "9995  5.060924\n",
      "9996  4.990597\n",
      "9997  5.008802\n",
      "9998  4.979198\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "results = []\n",
    "for n in range(1,10000):\n",
    "    nums = np.random.randint(low=1,high=10, size=n) # choose n numbers between 1 and 10\n",
    "    mean = nums.mean()                              # find the average of these numbers\n",
    "    results.append(mean)                            # add the average to a running list\n",
    "    \n",
    "# POP QUIZ: low large is the list results?\n",
    "\n",
    "\n",
    "\n",
    "len(results) # 9999\n",
    "# This was tricky because i took the range from 1 to 10000 and usually we do from 0 to 10000\n",
    "\n",
    "df = pd.DataFrame({ 'means' : results})\n",
    "\n",
    "print df.head() # the averages in the beginning are all over the place!\n",
    "# means\n",
    "# 9.0\n",
    "# 5.0\n",
    "# 6.0\n",
    "# 4.5\n",
    "# 4.0\n",
    "\n",
    "\n",
    "print df.tail() # as n, our size of the sample size, increases, the averages get closer to 5!\n",
    "\n",
    "# means\n",
    "# 4.998799\n",
    "# 5.060924\n",
    "# 4.990597\n",
    "# 5.008802\n",
    "# 4.979198\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111c16c10>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d7fc910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(title='Law of Large Numbers')\n",
    "plt.xlabel(\"Number of throws in sample\")\n",
    "plt.ylabel(\"Average Of Sample\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}