poisson_distribution_using_scipy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_theme(style='whitegrid')\n",
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On a booking counter on the average 3.6 people come in every 10 minutes on weekends. What is the probability of getting 7 people in 10 minutes ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04248414026930935"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.pmf(7, 3.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ### On a booking counter on the average 3.6 people come in every 10 minutes on weekends. What is the probability of getting 7 or less people in 10 minutes ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9692107246403425"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.cdf(7, 3.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ### On a booking counter on the average 3.6 people come in every 10 minutes on weekends. What is the probability of getting more than 7 people in 10 minutes ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.030789275359657444"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson.sf(7, 3.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On a booking counter on the average 3.6 people come in every 10 minutes on weekends. Plot a graph to show the probability of having 0 people in 10 minutes, 1 people in 10 minutes, 2 people in 10 minutes.... 10 people in 10 minutes in the queue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_axis = np.arange(0,11)\n",
    "x_axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.73237224,  9.83654008, 17.70577215, 21.24692658, 19.12223392,\n",
       "       13.76800842,  8.26080505,  4.24841403,  1.91178631,  0.76471452,\n",
       "        0.27529723])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_axis = poisson.pmf(x_axis, 3.6)\n",
    "y_axis = y_axis*100 # rescaling\n",
    "y_axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x=x_axis, y= y_axis)\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}