{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2000216737494469"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "random.choice([1,2,3,4]) # picks values with equal probability\n",
    "random.random() # selects \"random\" number between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Sample a boolean value\n",
    "# where the probability of True is 'prob'\n",
    "def sample(prob): \n",
    "    if random.random() < prob:\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.75002563\n"
     ]
    }
   ],
   "source": [
    "# Law of large numbers\n",
    "\n",
    "number_true = 0\n",
    "number_false = 0\n",
    "\n",
    "for i in range(100000000):\n",
    "    if sample(.75) == True:\n",
    "        number_true += 1\n",
    "    else:\n",
    "        number_false += 1\n",
    "print(number_true / (number_true + number_false) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.40012186\n"
     ]
    }
   ],
   "source": [
    "# Expected value\n",
    "numerator = 0\n",
    "denominator = 0\n",
    "\n",
    "# E[X] = 0.1*5 + 0.9*-1 = -.40\n",
    "\n",
    "for i in range(100000000):\n",
    "    if sample(0.1) == True:\n",
    "        numerator += 5.0\n",
    "        denominator += 1\n",
    "    else:\n",
    "        numerator += -1.0\n",
    "        denominator += 1\n",
    "print(numerator / denominator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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