{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "68bfdc75-bb40-4cb1-b37a-67104a17078d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dbb45e9e-e59b-45c7-ba03-ab762478bea3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8333333333333335\n"
     ]
    }
   ],
   "source": [
    "### Uniform Distribution (1-6 Dice)\n",
    "# Number of samples in one Repetition\n",
    "N=30\n",
    "# Number of Repetitions\n",
    "M=1\n",
    "a = np.random.randint(1,7,size=(N,M))\n",
    "m = np.mean(a)\n",
    "plt.hist(a,bins=np.arange(1,7+1)-.5)\n",
    "plt.vlines(m,0,N/6,colors=\"k\")\n",
    "plt.show()\n",
    "plt.close()\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5153fd89-6ecf-4e03-8fd3-00b6c3b7eca3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.66666667 3.5        3.9        ... 4.         3.66666667 4.        ]\n"
     ]
    }
   ],
   "source": [
    "# Number of samples in one Repetition\n",
    "N=30\n",
    "# Number of Repetitions\n",
    "M=10000\n",
    "a = np.random.randint(1,7,size=(N,M))\n",
    "m = np.mean(a,axis=0)\n",
    "binWidth = 1/N\n",
    "bins = np.arange(1,7+binWidth,binWidth)-binWidth/2\n",
    "plt.hist(m,bins=bins,color=\"darkcyan\")\n",
    "std = np.std(np.arange(1,7))/np.sqrt(N)\n",
    "mean = np.mean(np.arange(1,7))\n",
    "x = np.arange(0,8,.01)\n",
    "gaussianFunction = (1/(std*np.sqrt(2*np.pi)))*np.exp(-(x-mean)**2/(2*std**2))\n",
    "plt.plot(x,gaussianFunction*M*binWidth)\n",
    "plt.xlim(1,6)\n",
    "plt.show()\n",
    "plt.close()\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c4da75e0-5f37-4d74-900a-b699452032a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1223309023643744\n"
     ]
    }
   ],
   "source": [
    "### Exponential Distribution\n",
    "# Number of samples in one Repetition\n",
    "N=100\n",
    "# Number of Repetitions\n",
    "M=1\n",
    "a = np.random.exponential(size=(N,M))\n",
    "m = np.mean(a)\n",
    "plt.hist(a,bins=np.arange(0,5,.2)-.01)\n",
    "plt.vlines(m,0,N/10,colors=\"k\")\n",
    "plt.show()\n",
    "plt.close()\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "28beb913-4b64-40f9-8a05-8aa35671cfde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of samples in one Repetition\n",
    "N=30 #5,10,30\n",
    "# Number of Repetitions\n",
    "M=10000\n",
    "a = np.random.exponential(size=(N,M))\n",
    "m = np.mean(a,axis=0)\n",
    "binWidth = 1/N\n",
    "bins = np.arange(0,8+binWidth,binWidth)-binWidth/2\n",
    "plt.hist(m,bins=bins,color=\"darkcyan\")\n",
    "std = 1/np.sqrt(N)\n",
    "mean = 1\n",
    "x = np.arange(0,2,.001)\n",
    "gaussianFunction = (1/(std*np.sqrt(2*np.pi)))*np.exp(-(x-mean)**2/(2*std**2))\n",
    "plt.plot(x,gaussianFunction*M*binWidth)\n",
    "plt.xlim(mean-5*std,mean+5*std)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3cda0e0-e079-44e9-ad5b-cae0f5ab5bfe",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}