{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hughes and Hase worked example 3.2.2 (p. 25)\n",
    "### Using tools from the `stats` submodule of `scipy`\n",
    "\n",
    "Sampling resistors from a normal distribution with $\\bar{R} = 100\\, \\Omega$ and $\\sigma = 2\\, \\Omega$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np      # import numpy\n",
    "from scipy import stats # import stats sub-module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of selection a resistor with a value of $95\\, \\Omega$ or less\n",
    "\n",
    "$$\n",
    "P = \\int_{-\\infty}^{95} P_{DF}(R)\\, dR \\equiv C_{DF}(R)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probability =  0.006209665325776132\n"
     ]
    }
   ],
   "source": [
    "mean = 100\n",
    "sigma = 2\n",
    "\n",
    "p = stats.norm.cdf(95, mean, sigma)\n",
    "print('probability = ',p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This probability agrees with that given by H&H."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of selection a resistor with a value in the range $99-101\\, \\Omega$\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "P &=& \\int_{99}^{101} P_{DF}(R)\\, dR\\\\\n",
    "    &=& \\int_{-\\infty}^{101}P_{DF}(R)\\, dR - \\int_{-\\infty}^{99} P_{DF}(R)\\, dR \\\\\n",
    "    &=& C_{DF}(101) - C_{DF}(99)\n",
    "\\end{eqnarray*}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probability =  0.38292492254802624\n"
     ]
    }
   ],
   "source": [
    "p  = stats.norm.cdf(101, mean, sigma)   - stats.norm.cdf(99, mean, sigma)\n",
    "print('probability = ',p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This probability agrees with that given by H&H."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.7.7 64bit [GCC 7.3.0]"
        },
        {
         "module": "IPython",
         "version": "7.16.1"
        },
        {
         "module": "OS",
         "version": "Linux 4.9.0 9 amd64 x86_64 with debian 9.13"
        },
        {
         "module": "numpy",
         "version": "1.18.5"
        },
        {
         "module": "scipy",
         "version": "1.5.0"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.7.7 64bit [GCC 7.3.0]</td></tr><tr><td>IPython</td><td>7.16.1</td></tr><tr><td>OS</td><td>Linux 4.9.0 9 amd64 x86_64 with debian 9.13</td></tr><tr><td>numpy</td><td>1.18.5</td></tr><tr><td>scipy</td><td>1.5.0</td></tr><tr><td colspan='2'>Wed Aug 26 13:54:36 2020 EDT</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.7.7 64bit [GCC 7.3.0] \\\\ \\hline\n",
       "IPython & 7.16.1 \\\\ \\hline\n",
       "OS & Linux 4.9.0 9 amd64 x86\\_64 with debian 9.13 \\\\ \\hline\n",
       "numpy & 1.18.5 \\\\ \\hline\n",
       "scipy & 1.5.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Wed Aug 26 13:54:36 2020 EDT} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.7.7 64bit [GCC 7.3.0]\n",
       "IPython 7.16.1\n",
       "OS Linux 4.9.0 9 amd64 x86_64 with debian 9.13\n",
       "numpy 1.18.5\n",
       "scipy 1.5.0\n",
       "Wed Aug 26 13:54:36 2020 EDT"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information numpy, scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}