Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampleStdNormal(N):\n",
    "    sample = np.random.randn(N)\n",
    "    return np.mean(sample)\n",
    "   \n",
    "NSamplings=  1000\n",
    "meansperSample = []\n",
    "for i in range(NSamplings):    \n",
    "    sampleSize = 50\n",
    "    meansperSample.append(sampleStdNormal(sampleSize))\n",
    "\n",
    "print(f\"Mean of Means: {np.mean(meansperSample)}\")\n",
    "print(f\"Variance of Means: {np.var(meansperSample)}\")\n",
    "print(f\"Median of Means: {np.median(meansperSample)}\")\n",
    "\n",
    "\n",
    "plt.hist(meansperSample)\n",
    "plt.title(\"Histogram\")\n",
    "plt.show()\n",
    "plt.boxplot(meansperSample)\n",
    "plt.title(\"BoxPlot\")\n",
    "plt.show()\n",
    "sns.distplot(meansperSample).set_title(\"DIstribution\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sampleExponential(mean,N):\n",
    "    sample = np.random.exponential(mean,(N,1))\n",
    "    return np.mean(sample)\n",
    "   \n",
    "NSamplings=  1000\n",
    "meansperSample = []\n",
    "for i in range(NSamplings):    \n",
    "    sampleSize = 50\n",
    "    meansperSample.append(sampleExponential(1,sampleSize))\n",
    "\n",
    "print(f\"Mean of Means: {np.mean(meansperSample)}\")\n",
    "print(f\"Variance of Means: {np.var(meansperSample)}\")\n",
    "print(f\"Median of Means: {np.median(meansperSample)}\")\n",
    "\n",
    "\n",
    "plt.hist(meansperSample)\n",
    "plt.title(\"Histogram\")\n",
    "plt.show()\n",
    "plt.boxplot(meansperSample)\n",
    "plt.title(\"BoxPlot\")\n",
    "plt.show()\n",
    "sns.distplot(meansperSample).set_title(\"DIstribution\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "populationMean = 1\n",
    "SampleSize = 10000\n",
    "# expSamples = np.random.exponential(size=SampleSize)\n",
    "expSamples = np.random.exponential(populationMean,(SampleSize,1))\n",
    "sns.distplot(expSamples).set_title(f\"Emprical distribution of {SampleSize} samples drawn from Exp(mean={populationMean})\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "SampleSize = 1000\n",
    "stdNormalSamples = np.random.randn(SampleSize)\n",
    "sns.distplot(stdNormalSamples).set_title(f\"Emprical distribution of {SampleSize} samples drawn from a Std Normal Distribution\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulateGamev1(W,B):    \n",
    "    N = W+B\n",
    "    if N==1:\n",
    "        return (W,B)\n",
    "    else:\n",
    "        if W>1 and B>1:\n",
    "            availableChoices = ['W','B']\n",
    "            B1 = random.choice(availableChoices)\n",
    "            B2=random.choice(availableChoices)                        \n",
    "        \n",
    "        if W==1 and B>1:\n",
    "            availableChoices = ['W','B']\n",
    "            B1 = random.choice(['W','B'])\n",
    "            if B1 == 'W':\n",
    "                B2 = 'B'\n",
    "            else:\n",
    "                B2=random.choice(['W','B'])\n",
    "            \n",
    "        if W>1 and B==1:\n",
    "            availableChoices = ['W','B']\n",
    "            B1 = random.choice(['W','B'])\n",
    "            if B1 == 'B':\n",
    "                B2 = 'W'\n",
    "            else:\n",
    "                B2=random.choice(['W','B'])\n",
    "        \n",
    "        if W==0 and B>1:\n",
    "            B1='B'\n",
    "            B2 = 'B'\n",
    "            \n",
    "        if B==0 and W>1:\n",
    "            B1='W'\n",
    "            B2 = 'W'\n",
    "        \n",
    "        if B==1 and W==1:            \n",
    "            B1 = random.choice(['W','B'])\n",
    "            if B1 == 'B':\n",
    "                B2 = 'W'\n",
    "            else:\n",
    "                B2='B'\n",
    "        \n",
    "        if B1+B2 == 'WW':\n",
    "                W-=1\n",
    "        elif B1+B2 == 'BB':\n",
    "                B-=2\n",
    "                W+=1\n",
    "        else:\n",
    "             W-=1\n",
    "        \n",
    "        return simulateGamev1(W,B)\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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     ]
    }
   ],
   "source": [
    "for w in range(1,100):\n",
    "    print(simulateGamev1(w,21))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulateParty(N):    \n",
    "    duplicates = {}    \n",
    "    for i in range(1,N):    \n",
    "        day = random.randint(1,365)        \n",
    "        if day in list(duplicates.keys()):\n",
    "            duplicates[day]+=1\n",
    "        else:\n",
    "            duplicates[day]=1\n",
    "    \n",
    "    return max(duplicates.values())\n",
    "\n",
    "NPeople = list(range(2,100))\n",
    "Nsimulations = 1000\n",
    "probVsN = []\n",
    "\n",
    "for N in NPeople:\n",
    "    countVsN = []\n",
    "\n",
    "    for simulationNo in range(Nsimulations):\n",
    "        result = simulateParty(N)\n",
    "        countVsN.append(result>1)\n",
    "        \n",
    "#     print(countVsN)\n",
    "    probVsN.append(countVsN.count(True)/Nsimulations)\n",
    "        \n",
    "for i in range(len(probVsN)):\n",
    "    if probVsN[i]>0.5:\n",
    "        break\n",
    "\n",
    "\n",
    "plt.plot(NPeople,probVsN)\n",
    "plt.title(f\"{Nsimulations} simulations per N\")\n",
    "plt.show()    \n",
    "\n",
    "print(f\"50% probability occurs first at N = {i} people\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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