probability_mass_functions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import numerical and graphing libraries! Set the random seed for reproducability and precision for printing floats sensibly and tell the matplotlib backend to plot the graphs autmatically. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.set_printoptions(precision=2)\n",
    "np.random.seed(1)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually I'd reccoment using ```numpy.random.randint()``` but in this case it easier to explain what is going by being slightly more explicit.\n",
    "\n",
    "Here ```elements``` is the set { 1, 2, 3, 4, 5, 6 } of random states that a dice can take when it is rolled. We can assign the probability of each respective state in the ```probabilities``` array.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "elements: [1 2 3 4 5 6] \n",
      "probability weightings: [ 0.17  0.17  0.17  0.17  0.17  0.17] \n",
      "sum of weightings is basically one: True\n"
     ]
    }
   ],
   "source": [
    "elements = np.arange(1, 7)\n",
    "amount = len(elements)\n",
    "probabilities = np.array([1.0 / amount for _ in range(amount)])\n",
    "\n",
    "print(\"elements:\", elements,\n",
    "      \"\\nprobability weightings:\", probabilities,\n",
    "      \"\\nsum of weightings is basically one:\", np.isclose(1.0, probabilities.sum()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can make the random rolls and draw the histogram and look at the spread of what was actually rolled. The spread isn't absolutely perfect but more or less uniform. \n",
    "\n",
    "You can set the value ```normed``` (and in newer versions of numpy ```density```) to ```python \n",
    "True``` turn the histogram into a probability mass function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c41365f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "amount_rolls = 24000\n",
    "random_rolls = np.random.choice(elements, \n",
    "                                amount_rolls, \n",
    "                                p=probabilities)\n",
    "_ = plt.hist(random_rolls, bins=6, normed=True)\n",
    "_ = plt.xlabel(\"dice state\")\n",
    "_ = plt.ylabel(\"amount of rolls\")\n",
    "_ = plt.xlim(0, 7)"
   ]
  }
 ],
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