Introduction_to_Probability_in_Python.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 855
        },
        "id": "2MGcLdaepZno",
        "outputId": "7f88c22b-022e-49a0-b6ec-0ced22c25ae9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sample Mean: 0.04306406203997476\n",
            "Sample Standard Deviation: 1.011946429011456\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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OnDHsdrvx+uuvm1rTN99843Qjdx48ePDgwYMHDx718/HNN99ctbZz61cLX7x4Udu2bVNycrKjzcPDQ7GxscrOzr7iuDlz5igoKEgTJkzQRx995PTc4cOHlZubq9jYWEdbs2bNFBMTo+zsbI0ePbrcfEVFRY7vi5fk+E75w4cPq0mTJqbOpbi4WBs3btStt94qLy8vU2MaKmJlDnEyhziZQ5zMIU7mECfziJU5rsTp3LlzioyMNFWrubXg/e6771RSUqLg4GCn9uDgYH355ZcVjvn444/1f//3f9qxY0eFz+fm5jrmuHzOsucul5aWptTU1HLt2dnZ8vPzu9ppOPj5+SknJ8d0/4aMWJlDnMwhTuYQJ3OIkznEyTxiZU5V41RYWChJprafurXgrapz587pvvvu04svvqjAwMAamzc5OVlJSUmO4/z8fLVq1UpDhgxR06ZNTc1RXFysjIwMDR48mP/BXQWxMoc4mUOczCFO5hAnc4iTecTKHFfilJ+fb3p+txa8gYGB8vT0VF5enlN7Xl6eQkJCyvU/dOiQjhw5ot/85jeOttLSUklSo0aNtH//fse4vLw8hYaGOs0ZFRVV4Trsdrvsdnu5di8vryonpytjGipiZQ5xMoc4mUOczCFO5hAn84iVOVWJU1Xi6dbbknl7e6tnz57KzMx0tJWWliozM1O9e/cu179jx47atWuXduzY4Xj89re/1a233qodO3aoVatWioyMVEhIiNOc+fn5ysnJqXBOAAAAWJvbtzQkJSUpPj5e0dHR6tWrl9LT01VQUKCEhARJ0rhx4xQeHq60tDT5+PioS5cuTuObN28uSU7tU6dO1bx589S+fXvHbcnCwsLK3a8XAAAA1uf2gnfUqFE6deqUZs2apdzcXEVFRWndunWOD50dPXr06vdWu8y0adNUUFCgBx98UGfOnFHfvn21bt06U/fgBQAAgLW4veCVpMTERCUmJlb4XFZWVqVjX3755XJtNptNc+bM0Zw5c2pgdQAAALiW1YuvFgYAAABqCwUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApdWLuzQAAICGI2L6e+5eQp2xexpa0EvqkrJeRSU2dy+n1h15epi7l1AhrvACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBpFLwAAACwNApeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsrV4UvIsXL1ZERIR8fHwUExOjrVu3XrHvO++8o+joaDVv3lyNGzdWVFSUVq5c6dRn/PjxstlsTo+hQ4fW9mkAAACgHmrk7gWsWbNGSUlJWrp0qWJiYpSenq64uDjt379fQUFB5fq3aNFCf/jDH9SxY0d5e3vrn//8pxISEhQUFKS4uDhHv6FDh2r58uWOY7vdXifnAwAAgPrF7Vd4Fy1apIkTJyohIUGdO3fW0qVL5efnp2XLllXYf8CAAbrjjjvUqVMntW3bVlOmTFG3bt308ccfO/Wz2+0KCQlxPAICAuridAAAAFDPuPUK78WLF7Vt2zYlJyc72jw8PBQbG6vs7OyrjjcMQxs2bND+/fs1f/58p+eysrIUFBSkgIAADRw4UPPmzdN1111X4TxFRUUqKipyHOfn50uSiouLVVxcbOpcyvqZ7d+QEStziJM5xMkc4mQOcTKnunGyexo1uZx6ze5hOP1pda7mhCs5VZW+NsMw3PYvcPz4cYWHh2vLli3q3bu3o33atGnatGmTcnJyKhx39uxZhYeHq6ioSJ6ennrhhRd0//33O55fvXq1/Pz8FBkZqUOHDmnGjBny9/dXdna2PD09y82XkpKi1NTUcu2rVq2Sn59fDZwpAAAAalJhYaHGjh2rs2fPqmnTppX2dfseXlc0adJEO3bs0Pnz55WZmamkpCS1adNGAwYMkCSNHj3a0bdr167q1q2b2rZtq6ysLA0aNKjcfMnJyUpKSnIc5+fnq1WrVhoyZMhVA1imuLhYGRkZGjx4sLy8vKp3ghZHrMwhTuYQJ3OIkznEyZzqxqlLyvpaWFX9ZPcwNDe6VDM/81BRqc3dy6l1u1Pirt6pAq7kVNlv5M1wa8EbGBgoT09P5eXlObXn5eUpJCTkiuM8PDzUrl07SVJUVJT27duntLQ0R8F7uTZt2igwMFAHDx6ssOC12+0VfqjNy8uryj/IroxpqIiVOcTJHOJkDnEyhziZ42qcikqsX/hdrqjU1iDOu7o/N1XJqaq8lls/tObt7a2ePXsqMzPT0VZaWqrMzEynLQ5XU1pa6rQH93LHjh3T6dOnFRoaWq31AgAA4Nrj9i0NSUlJio+PV3R0tHr16qX09HQVFBQoISFBkjRu3DiFh4crLS1NkpSWlqbo6Gi1bdtWRUVFev/997Vy5UotWbJEknT+/HmlpqZq5MiRCgkJ0aFDhzRt2jS1a9fO6bZlAAAAaBjcXvCOGjVKp06d0qxZs5Sbm6uoqCitW7dOwcHBkqSjR4/Kw+O/F6ILCgo0adIkHTt2TL6+vurYsaNeffVVjRo1SpLk6empnTt3asWKFTpz5ozCwsI0ZMgQzZ07l3vxAgAANEBuL3glKTExUYmJiRU+l5WV5XQ8b948zZs374pz+fr6av36hrMZHgAAAJVz+xdPAAAAALWJghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEuj4AUAAIClUfACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBpFLwAAACwNApeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKXVi4J38eLFioiIkI+Pj2JiYrR169Yr9n3nnXcUHR2t5s2bq3HjxoqKitLKlSud+hiGoVmzZik0NFS+vr6KjY3VgQMHavs0AAAAUA+5veBds2aNkpKSNHv2bG3fvl3du3dXXFycTp48WWH/Fi1a6A9/+IOys7O1c+dOJSQkKCEhQevXr3f0WbBggZ577jktXbpUOTk5aty4seLi4nThwoW6Oi0AAADUE24veBctWqSJEycqISFBnTt31tKlS+Xn56dly5ZV2H/AgAG644471KlTJ7Vt21ZTpkxRt27d9PHHH0v66epuenq6nnzySQ0fPlzdunXTK6+8ouPHj2vt2rV1eGYAAACoDxq588UvXryobdu2KTk52dHm4eGh2NhYZWdnX3W8YRjasGGD9u/fr/nz50uSDh8+rNzcXMXGxjr6NWvWTDExMcrOztbo0aPLzVNUVKSioiLHcX5+viSpuLhYxcXFps6lrJ/Z/g0ZsTKHOJlDnMwhTuYQJ3OqGye7p1GTy6nX7B6G059W52pOuJJTVelrMwzDbf8Cx48fV3h4uLZs2aLevXs72qdNm6ZNmzYpJyenwnFnz55VeHi4ioqK5OnpqRdeeEH333+/JGnLli265ZZbdPz4cYWGhjrG3HPPPbLZbFqzZk25+VJSUpSamlqufdWqVfLz86vuaQIAAKCGFRYWauzYsTp79qyaNm1aaV+3XuF1VZMmTbRjxw6dP39emZmZSkpKUps2bTRgwACX5ktOTlZSUpLjOD8/X61atdKQIUOuGsAyxcXFysjI0ODBg+Xl5eXSOhoKYmVOdePUJWX91TtZgN3D0NzoUs38zENFpTZ3L6fW7U6Jc2kcP3fmECdzeH8yj/coc1zJqbLfyJvh1oI3MDBQnp6eysvLc2rPy8tTSEjIFcd5eHioXbt2kqSoqCjt27dPaWlpGjBggGNcXl6e0xXevLw8RUVFVTif3W6X3W4v1+7l5VXlH2RXxjRUxMocV+NUVGL9N9afKyq1NYhzru7PDD935hAnc3h/Mo/3KPPjzc5Rlddy64fWvL291bNnT2VmZjraSktLlZmZ6bTF4WpKS0sde3AjIyMVEhLiNGd+fr5ycnKqNCcAAACswe1bGpKSkhQfH6/o6Gj16tVL6enpKigoUEJCgiRp3LhxCg8PV1pamiQpLS1N0dHRatu2rYqKivT+++9r5cqVWrJkiSTJZrNp6tSpmjdvntq3b6/IyEjNnDlTYWFhGjFihLtOEwAAAG7i9oJ31KhROnXqlGbNmqXc3FxFRUVp3bp1Cg4OliQdPXpUHh7/vRBdUFCgSZMm6dixY/L19VXHjh316quvatSoUY4+06ZNU0FBgR588EGdOXNGffv21bp16+Tj41Pn5wcAAAD3cnvBK0mJiYlKTEys8LmsrCyn43nz5mnevHmVzmez2TRnzhzNmTOnppYIAACAa5Tbv3gCAAAAqE0UvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBpFLwAAACwNApeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEuj4AUAAIClUfACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYWr0oeBcvXqyIiAj5+PgoJiZGW7duvWLfF198Uf369VNAQIACAgIUGxtbrv/48eNls9mcHkOHDq3t0wAAAEA95PaCd82aNUpKStLs2bO1fft2de/eXXFxcTp58mSF/bOysjRmzBht3LhR2dnZatWqlYYMGaJvv/3Wqd/QoUN14sQJx+P111+vi9MBAABAPeP2gnfRokWaOHGiEhIS1LlzZy1dulR+fn5atmxZhf1fe+01TZo0SVFRUerYsaNeeukllZaWKjMz06mf3W5XSEiI4xEQEFAXpwMAAIB6ppE7X/zixYvatm2bkpOTHW0eHh6KjY1Vdna2qTkKCwtVXFysFi1aOLVnZWUpKChIAQEBGjhwoObNm6frrruuwjmKiopUVFTkOM7Pz5ckFRcXq7i42NQ6yvqZ7d+QEStzqhsnu6dRk8upt+wehtOfVudqPvBzZw5xMof3J/N4j6rauKqMr0pfm2EYbvsXOH78uMLDw7Vlyxb17t3b0T5t2jRt2rRJOTk5V51j0qRJWr9+vfbs2SMfHx9J0urVq+Xn56fIyEgdOnRIM2bMkL+/v7Kzs+Xp6VlujpSUFKWmppZrX7Vqlfz8/KpxhgAAAKgNhYWFGjt2rM6ePaumTZtW2tetV3ir6+mnn9bq1auVlZXlKHYlafTo0Y6/d+3aVd26dVPbtm2VlZWlQYMGlZsnOTlZSUlJjuP8/HzH3uCrBbBMcXGxMjIyNHjwYHl5eVXjrKyPWJlT3Th1SVlfC6uqf+wehuZGl2rmZx4qKrW5ezm1bndKnEvj+LkzhziZw/uTebxHmeNKTpX9Rt4Mtxa8gYGB8vT0VF5enlN7Xl6eQkJCKh27cOFCPf300/rwww/VrVu3Svu2adNGgYGBOnjwYIUFr91ul91uL9fu5eVV5R9kV8Y0VMTKHFfjVFRi/TfWnysqtTWIc67uzww/d+YQJ3N4fzKP9yjz483OUZXXculDaxs3bnRlWDne3t7q2bOn0wfOyj6A9vMtDpdbsGCB5s6dq3Xr1ik6Ovqqr3Ps2DGdPn1aoaGhNbJuAAAAXDtcKniHDh2qtm3bat68efrmm2+qtYCkpCS9+OKLWrFihfbt26eHHnpIBQUFSkhIkCSNGzfO6UNt8+fP18yZM7Vs2TJFREQoNzdXubm5On/+vCTp/PnzeuKJJ/Tpp5/qyJEjyszM1PDhw9WuXTvFxbl2mR0AAADXLpcK3m+//VaJiYl666231KZNG8XFxemNN97QxYsXqzzXqFGjtHDhQs2aNUtRUVHasWOH1q1bp+DgYEnS0aNHdeLECUf/JUuW6OLFi7rrrrsUGhrqeCxcuFCS5OnpqZ07d+q3v/2tbrzxRk2YMEE9e/bURx99VOG2BQAAAFibS3t4AwMD9eijj+rRRx/V9u3btXz5ck2aNEmTJk3S2LFjNWHCBHXv3t30fImJiUpMTKzwuaysLKfjI0eOVDqXr6+v1q9vOJvhAQAAULlqf/FEjx49lJycrMTERJ0/f17Lli1Tz5491a9fP+3Zs6cm1ggAAAC4zOWCt7i4WG+99ZZuu+02tW7dWuvXr9fzzz+vvLw8HTx4UK1bt9bdd99dk2sFAAAAqsylLQ0PP/ywXn/9dRmGofvuu08LFixQly5dHM83btxYCxcuVFhYWI0tFAAAAHCFSwXv3r179b//+7+68847r/hBsMDAwBq7fRkAAADgKpe2NMyePVt33313uWL30qVL2rx5sySpUaNG6t+/f/VXCAAAAFSDSwXvrbfequ+//75c+9mzZ3XrrbdWe1EAAABATXGp4DUMQzZb+a/HO336tBo3blztRQEAAAA1pUp7eO+8805Jks1m0/jx4522NJSUlGjnzp3q06dPza4QAAAAqIYqFbzNmjWT9NMV3iZNmsjX19fxnLe3t375y19q4sSJNbtCAAAAoBqqVPAuX75ckhQREaHHH3+c7QsAAACo91y6Ldns2bNreh0AAABArTBd8Pbo0UOZmZkKCAjQzTffXOGH1sps3769RhYHAAAAVJfpgnf48OGOD6mNGDGittYDAAAA1CjTBe/PtzGwpQEAAADXCpfuwwsAAABcK0xf4Q0ICKh03+7PVfQtbAAAAIA7mC5409PTa3EZAAAAQO0wXfDGx8fX5joAAACAWmG64M3Pz1fTpk0df69MWT8AAADA3aq0h/fEiRMKCgpS8+bNK9zPaxiGbDabSkpKanSRAAAAgKtMF7wbNmxQixYtJEkbN26stQUBAAAANcl0wdu/f/8K/w4AAADUZ6YL3sv98MMP+r//+z/t27dPktS5c2clJCQ4rgIDAAAA9YFLXzyxefNmRURE6LnnntMPP/ygH374Qc8995wiIyO1efPmml4jAAAA4DKXrvBOnjxZo0aN0pIlS+Tp6SlJKikp0aRJkzR58mTt2rWrRhcJAHCviOnvuXsJdcLuaWhBL6lLynoVlZj7sqVr3ZGnh7l7CUCtc+kK78GDB/XYY485il1J8vT0VFJSkg4ePFhjiwMAAACqy6WCt0ePHo69uz+3b98+de/evdqLAgAAAGqK6YJ3586djscjjzyiKVOmaOHChfr444/18ccfa+HChXr00Uf16KOPVnkRixcvVkREhHx8fBQTE6OtW7dese+LL76ofv36KSAgQAEBAYqNjS3X3zAMzZo1S6GhofL19VVsbKwOHDhQ5XUBAADg2md6D29UVJRsNpsMw3C0TZs2rVy/sWPHatSoUaYXsGbNGiUlJWnp0qWKiYlRenq64uLitH//fgUFBZXrn5WVpTFjxqhPnz7y8fHR/PnzNWTIEO3Zs0fh4eGSpAULFui5557TihUrFBkZqZkzZyouLk579+6Vj4+P6bUBAADg2me64D18+HCtLGDRokWaOHGiEhISJElLly7Ve++9p2XLlmn69Onl+r/22mtOxy+99JLefvttZWZmaty4cTIMQ+np6XryySc1fPhwSdIrr7yi4OBgrV27VqNHj66V8wAAAED9ZLrgbd26dY2/+MWLF7Vt2zYlJyc72jw8PBQbG6vs7GxTcxQWFqq4uNhx/9/Dhw8rNzdXsbGxjj7NmjVTTEyMsrOzKyx4i4qKVFRU5DjOz8+XJBUXF6u4uNjUOsr6me3fkBErc6obJ7uncfVOFmD3MJz+tDpX84F8Mqeh5ZPkWk6QT+Y1tJyqy/eoqvS1GT/fo1BFe/fu1dGjR3Xx4kWn9t/+9remxh8/flzh4eHasmWLevfu7WifNm2aNm3apJycnKvOMWnSJK1fv1579uyRj4+PtmzZoltuuUXHjx9XaGioo98999wjm82mNWvWlJsjJSVFqamp5dpXrVolPz8/U+cCAACAulNYWKixY8fq7Nmzatq0aaV9XboP73/+8x/dcccd2rVrl9O+Xpvtp3sWlpSUuDJtlT399NNavXq1srKyqrU3Nzk5WUlJSY7j/Px8tWrVSkOGDLlqAMsUFxcrIyNDgwcPlpeXl8traQiIlTnVjVOXlPW1sKr6x+5haG50qWZ+5qGiUuvfN3V3SpxL48gncxpaPkmu5RT5ZF5Dy6m6fI8q+428GS4VvFOmTFFkZKQyMzMVGRmprVu36vTp03rssce0cOFC0/MEBgbK09NTeXl5Tu15eXkKCQmpdOzChQv19NNP68MPP1S3bt0c7WXj8vLynK7w5uXlKSoqqsK57Ha77HZ7uXYvL68q/yC7MqahIlbmuBqnhnLT/DJFpbYGcc7V/Zkhn8xpKPkkVS+nyCfzGkpO1eV7VFVey6X78GZnZ2vOnDkKDAyUh4eHPDw81LdvX6WlpemRRx4xPY+3t7d69uypzMxMR1tpaakyMzOdtjhcbsGCBZo7d67WrVun6Ohop+ciIyMVEhLiNGd+fr5ycnIqnRMAAADW5NIV3pKSEjVp0kTST1dpjx8/rg4dOqh169bav39/leZKSkpSfHy8oqOj1atXL6Wnp6ugoMBx14Zx48YpPDxcaWlpkqT58+dr1qxZWrVqlSIiIpSbmytJ8vf3l7+/v2w2m6ZOnap58+apffv2jtuShYWFacSIEa6cLgAAAK5hLhW8Xbp00RdffKHIyEjFxMRowYIF8vb21l//+le1adOmSnONGjVKp06d0qxZs5Sbm6uoqCitW7dOwcHBkqSjR4/Kw+O/F6KXLFmiixcv6q677nKaZ/bs2UpJSZH004feCgoK9OCDD+rMmTPq27ev1q1bxz14AQAAGiCXCt4nn3xSBQUFkqQ5c+bo9ttvV79+/XTddddVeBeEq0lMTFRiYmKFz2VlZTkdHzly5Krz2Ww2zZkzR3PmzKnyWgAAAGAtLhW8cXH//QReu3bt9OWXX+r7779XQECA404NAAAAQH3gUsH7c998840kqVWrVtVeDAAAAFDTXLpLw6VLlzRz5kw1a9ZMERERioiIULNmzfTkk0/y7VkAAACoV1y6wvvwww/rnXfe0YIFCxy3+srOzlZKSopOnz6tJUuW1OgiAQAAAFe5VPCuWrVKq1ev1q9//WtHW7du3dSqVSuNGTOGghcAAAD1hktbGux2uyIiIsq1R0ZGytvbu7prAgAAAGqMSwVvYmKi5s6dq6KiIkdbUVGRnnrqqSveXgwAAABwB9NbGu68806n4w8//FDXX3+9unfvLkn64osvdPHiRQ0aNKhmVwgAAABUg+mCt1mzZk7HI0eOdDrmtmQAAACoj0wXvMuXL6/NdQAAAAC1olpfPHHq1Cnt379fktShQwe1bNmyRhYFAAAA1BSXPrRWUFCg+++/X6GhofrVr36lX/3qVwoLC9OECRNUWFhY02sEAAAAXOZSwZuUlKRNmzbpH//4h86cOaMzZ87ob3/7mzZt2qTHHnusptcIAAAAuMylLQ1vv/223nrrLQ0YMMDRdtttt8nX11f33HMPXzwBAACAesOlK7yFhYUKDg4u1x4UFMSWBgAAANQrLhW8vXv31uzZs3XhwgVH248//qjU1FT17t27xhYHAAAAVJdLWxrS09M1dOjQcl884ePjo/Xr19foAgEAAIDqcKng7dq1qw4cOKDXXntNX375pSRpzJgxuvfee+Xr61ujCwQAAACqo8oFb3FxsTp27Kh//vOfmjhxYm2sCQAAAKgxVd7D6+Xl5bR3FwAAAKjPXPrQ2uTJkzV//nxdunSpptcDAAAA1CiX9vD++9//VmZmpj744AN17dpVjRs3dnr+nXfeqZHFAQAAANXlUsHbvHlzjRw5sqbXAgAAANS4KhW8paWl+tOf/qSvvvpKFy9e1MCBA5WSksKdGQAAAFBvVWkP71NPPaUZM2bI399f4eHheu655zR58uTaWhsAAABQbVUqeF955RW98MILWr9+vdauXat//OMfeu2111RaWlpb6wMAAACqpUoF79GjR3Xbbbc5jmNjY2Wz2XT8+PEaXxgAAABQE6pU8F66dEk+Pj5ObV5eXiouLnZ5AYsXL1ZERIR8fHwUExOjrVu3XrHvnj17NHLkSEVERMhmsyk9Pb1cn5SUFNlsNqdHx44dXV4fAAAArm1V+tCaYRgaP3687Ha7o+3ChQv6/e9/73RrMrO3JVuzZo2SkpK0dOlSxcTEKD09XXFxcdq/f7+CgoLK9S8sLFSbNm10991369FHH73ivDfddJM+/PBDx3GjRi7djAIAAAAWUKVKMD4+vlzb7373O5dffNGiRZo4caISEhIkSUuXLtV7772nZcuWafr06eX6/+IXv9AvfvELSarw+TKNGjVSSEiIy+sCAACAdVSp4F2+fHmNvfDFixe1bds2JScnO9o8PDwUGxur7Ozsas194MABhYWFycfHR71791ZaWppuuOGGK/YvKipSUVGR4zg/P1+SVFxcbHq7Rlm/6mzvaCiIlTnVjZPd06jJ5dRbdg/D6U+rczUfyCdzGlo+Sa7lBPlkXkPLqbp8j6pKX5thGG75Fzh+/LjCw8O1ZcsW9e7d29E+bdo0bdq0STk5OZWOj4iI0NSpUzV16lSn9n/96186f/68OnTooBMnTig1NVXffvutdu/erSZNmlQ4V0pKilJTU8u1r1q1Sn5+flU/OQAAANSqwsJCjR07VmfPnlXTpk0r7Wu5za2//vWvHX/v1q2bYmJi1Lp1a73xxhuaMGFChWOSk5OVlJTkOM7Pz1erVq00ZMiQqwawTHFxsTIyMjR48GB5eXlV7yQsjliZU904dUlZXwurqn/sHobmRpdq5mceKiq1uXs5tW53SpxL48gncxpaPkmu5RT5ZF5Dy6m6fI8q+428GW4reAMDA+Xp6am8vDyn9ry8vBrdf9u8eXPdeOONOnjw4BX72O12pw/ilfHy8qryD7IrYxoqYmWOq3EqKrH+G+vPFZXaGsQ5V/dnhnwyp6Hkk1S9nCKfzGsoOVWX71FVea0q3ZasJnl7e6tnz57KzMx0tJWWliozM9Npi0N1nT9/XocOHVJoaGiNzQkAAIBrh1u3NCQlJSk+Pl7R0dHq1auX0tPTVVBQ4Lhrw7hx4xQeHq60tDRJP33Qbe/evY6/f/vtt9qxY4f8/f3Vrl07SdLjjz+u3/zmN2rdurWOHz+u2bNny9PTU2PGjHHPSQIAAMCt3Frwjho1SqdOndKsWbOUm5urqKgorVu3TsHBwZJ++mY3D4//XoQ+fvy4br75ZsfxwoULtXDhQvXv319ZWVmSpGPHjmnMmDE6ffq0WrZsqb59++rTTz9Vy5Yt6/TcAAAAUD+4/UNriYmJSkxMrPC5siK2TEREhK52U4nVq1fX1NIAAABgAW7bwwsAAADUBQpeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEuj4AUAAIClUfACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBpjdy9APwkYvp77l5CnbF7GlrQS+qSsl5FJTZ3L6fWHXl6mLuXAABAg8YVXgAAAFgaBS8AAAAsze0F7+LFixURESEfHx/FxMRo69atV+y7Z88ejRw5UhEREbLZbEpPT6/2nAAAALA2txa8a9asUVJSkmbPnq3t27ere/fuiouL08mTJyvsX1hYqDZt2ujpp59WSEhIjcwJAAAAa3Nrwbto0SJNnDhRCQkJ6ty5s5YuXSo/Pz8tW7aswv6/+MUv9Kc//UmjR4+W3W6vkTkBAABgbW67S8PFixe1bds2JScnO9o8PDwUGxur7OzsOp2zqKhIRUVFjuP8/HxJUnFxsYqLi029dlk/s/0vZ/c0XBp3LbJ7GE5/Wp2rOUFOmUM+VW0c+VS5hpZPkms5QT6Z19Byqi7fo6rS12YYhlv+BY4fP67w8HBt2bJFvXv3drRPmzZNmzZtUk5OTqXjIyIiNHXqVE2dOrXac6akpCg1NbVc+6pVq+Tn51fFMwMAAEBtKyws1NixY3X27Fk1bdq00r7ch1dScnKykpKSHMf5+flq1aqVhgwZctUAlikuLlZGRoYGDx4sLy+vKq+hS8r6Ko+5Vtk9DM2NLtXMzzxUVGr9+/DuTolzaRw5ZQ75ZA75ZE5DyyfJtZwin8xraDlVl+9RZb+RN8NtBW9gYKA8PT2Vl5fn1J6Xl3fFD6TV1px2u73CPcFeXl5V/kF2ZYykBvEFDJcrKrU1iPN2JR8uH09OXR35ZH48+XR1DSWfpOrlFPlkXkPJqbp8j6rKa7ntQ2ve3t7q2bOnMjMzHW2lpaXKzMx02o7g7jkBAABwbXPrloakpCTFx8crOjpavXr1Unp6ugoKCpSQkCBJGjdunMLDw5WWlibppw+l7d271/H3b7/9Vjt27JC/v7/atWtnak4AAAA0LG4teEeNGqVTp05p1qxZys3NVVRUlNatW6fg4GBJ0tGjR+Xh8d+L0MePH9fNN9/sOF64cKEWLlyo/v37Kysry9ScAAAAaFjc/qG1xMREJSYmVvhcWRFbJiIiQmZuKlHZnAAAAGhY3P7VwgAAAEBtouAFAACApVHwAgAAwNIoeAEAAGBpFLwAAACwNApeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEuj4AUAAIClUfACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBp9aLgXbx4sSIiIuTj46OYmBht3bq10v5vvvmmOnbsKB8fH3Xt2lXvv/++0/Pjx4+XzWZzegwdOrQ2TwEAAAD1lNsL3jVr1igpKUmzZ8/W9u3b1b17d8XFxenkyZMV9t+yZYvGjBmjCRMm6PPPP9eIESM0YsQI7d6926nf0KFDdeLECcfj9ddfr4vTAQAAQD3j9oJ30aJFmjhxohISEtS5c2ctXbpUfn5+WrZsWYX9n332WQ0dOlRPPPGEOnXqpLlz56pHjx56/vnnnfrZ7XaFhIQ4HgEBAXVxOgAAAKhnGrnzxS9evKht27YpOTnZ0ebh4aHY2FhlZ2dXOCY7O1tJSUlObXFxcVq7dq1TW1ZWloKCghQQEKCBAwdq3rx5uu666yqcs6ioSEVFRY7j/Px8SVJxcbGKi4tNnUtZP7P9L2f3NFwady2yexhOf1qdqzlBTplDPlVtHPlUuYaWT5JrOUE+mdfQcqou36Oq0tdmGIbb/gWOHz+u8PBwbdmyRb1793a0T5s2TZs2bVJOTk65Md7e3lqxYoXGjBnjaHvhhReUmpqqvLw8SdLq1avl5+enyMhIHTp0SDNmzJC/v7+ys7Pl6elZbs6UlBSlpqaWa1+1apX8/Pxq4lQBAABQgwoLCzV27FidPXtWTZs2rbSvW6/w1pbRo0c7/t61a1d169ZNbdu2VVZWlgYNGlSuf3JystNV4/z8fLVq1UpDhgy5agDLFBcXKyMjQ4MHD5aXl1eV19wlZX2Vx1yr7B6G5kaXauZnHioqtbl7ObVud0qcS+PIKXPIJ3PIJ3MaWj5JruUU+WReQ8upunyPKvuNvBluLXgDAwPl6enpuDJbJi8vTyEhIRWOCQkJqVJ/SWrTpo0CAwN18ODBCgteu90uu91ert3Ly6vKP8iujJGkohLr/xBcrqjU1iDO25V8uHw8OXV15JP58eTT1TWUfJKql1Pkk3kNJafq8j2qKq/l1g+teXt7q2fPnsrMzHS0lZaWKjMz02mLw8/17t3bqb8kZWRkXLG/JB07dkynT59WaGhozSwcAAAA1wy336UhKSlJL774olasWKF9+/bpoYceUkFBgRISEiRJ48aNc/pQ25QpU7Ru3To988wz+vLLL5WSkqLPPvtMiYmJkqTz58/riSee0KeffqojR44oMzNTw4cPV7t27RQX59pldgAAAFy73L6Hd9SoUTp16pRmzZql3NxcRUVFad26dQoODpYkHT16VB4e/63L+/Tpo1WrVunJJ5/UjBkz1L59e61du1ZdunSRJHl6emrnzp1asWKFzpw5o7CwMA0ZMkRz586tcNsCAAAArM3tBa8kJSYmOq7QXi4rK6tc291336277767wv6+vr5av77hbIYHAABA5dy+pQEAAACoTRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEuj4AUAAIClUfACAADA0ih4AQAAYGkUvAAAALA0Cl4AAABYGgUvAAAALI2CFwAAAJZGwQsAAABLo+AFAACApVHwAgAAwNIoeAEAAGBpFLwAAACwNApeAAAAWBoFLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFhavSh4Fy9erIiICPn4+CgmJkZbt26ttP+bb76pjh07ysfHR127dtX777/v9LxhGJo1a5ZCQ0Pl6+ur2NhYHThwoDZPAQAAAPWU2wveNWvWKCkpSbNnz9b27dvVvXt3xcXF6eTJkxX237Jli8aMGaMJEybo888/14gRIzRixAjt3r3b0WfBggV67rnntHTpUuXk5Khx48aKi4vThQsX6uq0AAAAUE+4veBdtGiRJk6cqISEBHXu3FlLly6Vn5+fli1bVmH/Z599VkOHDtUTTzyhTp06ae7cuerRo4eef/55ST9d3U1PT9eTTz6p4cOHq1u3bnrllVd0/PhxrV27tg7PDAAAAPVBI3e++MWLF7Vt2zYlJyc72jw8PBQbG6vs7OwKx2RnZyspKcmpLS4uzlHMHj58WLm5uYqNjXU836xZM8XExCg7O1ujR48uN2dRUZGKioocx2fPnpUkff/99youLjZ1LsXFxSosLNTp06fl5eVlaszPNbpUUOUx16pGpYYKC0vVqNhDJaU2dy+n1p0+fdqlceSUOeSTOeSTOQ0tnyTXcop8Mq+h5VRdvkedO3dO0k8XO6/GrQXvd999p5KSEgUHBzu1BwcH68svv6xwTG5uboX9c3NzHc+XtV2pz+XS0tKUmpparj0yMtLciaDKxrp7AXUo8Bl3r8D6yCfUpIaUTxI5VRcaUk65I5/OnTunZs2aVdrHrQVvfZGcnOx01bi0tFTff/+9rrvuOtls5v43lp+fr1atWumbb75R06ZNa2uplkCszCFO5hAnc4iTOcTJHOJkHrEyx5U4GYahc+fOKSws7Kp93VrwBgYGytPTU3l5eU7teXl5CgkJqXBMSEhIpf3L/szLy1NoaKhTn6ioqArntNvtstvtTm3Nmzevyqk4NG3alIQ2iViZQ5zMIU7mECdziJM5xMk8YmVOVeN0tSu7Zdz6oTVvb2/17NlTmZmZjrbS0lJlZmaqd+/eFY7p3bu3U39JysjIcPSPjIxUSEiIU5/8/Hzl5ORccU4AAABYl9u3NCQlJSk+Pl7R0dHq1auX0tPTVVBQoISEBEnSuHHjFB4errS0NEnSlClT1L9/fz3zzDMaNmyYVq9erc8++0x//etfJUk2m01Tp07VvHnz1L59e0VGRmrmzJkKCwvTiBEj3HWaAAAAcBO3F7yjRo3SqVOnNGvWLOXm5ioqKkrr1q1zfOjs6NGj8vD474XoPn36aNWqVXryySc1Y8YMtW/fXmvXrlWXLl0cfaZNm6aCggI9+OCDOnPmjPr27at169bJx8en1s7Dbrdr9uzZ5bZGoDxiZQ5xMoc4mUOczCFO5hAn84iVObUdJ5th5l4OAAAAwDXK7V88AQAAANQmCl4AAABYGgUvAAAALI2CFwAAAJZGwVsFixcvVkREhHx8fBQTE6OtW7dese/LL78sm83m9KjNu0TUF5s3b9ZvfvMbhYWFyWazae3atVcdk5WVpR49eshut6tdu3Z6+eWXa32d7lbVOGVlZZXLJ5vNdsWvy7aKtLQ0/eIXv1CTJk0UFBSkESNGaP/+/Vcd9+abb6pjx47y8fFR165d9f7779fBat3HlTg1xPeoJUuWqFu3bo4b2/fu3Vv/+te/Kh3T0HJJqnqcGmIuVeTpp5923Bq1Mg0xp37OTJxqI6coeE1as2aNkpKSNHv2bG3fvl3du3dXXFycTp48ecUxTZs21YkTJxyPr7/+ug5X7B4FBQXq3r27Fi9ebKr/4cOHNWzYMN16663asWOHpk6dqgceeEDr16+v5ZW6V1XjVGb//v1OORUUFFRLK6wfNm3apMmTJ+vTTz9VRkaGiouLNWTIEBUUFFxxzJYtWzRmzBhNmDBBn3/+uUaMGKERI0Zo9+7ddbjyuuVKnKSG9x51/fXX6+mnn9a2bdv02WefaeDAgRo+fLj27NlTYf+GmEtS1eMkNbxcuty///1v/eUvf1G3bt0q7ddQc6qM2ThJtZBTBkzp1auXMXnyZMdxSUmJERYWZqSlpVXYf/ny5UazZs3qaHX1kyTj3XffrbTPtGnTjJtuusmpbdSoUUZcXFwtrqx+MROnjRs3GpKMH374oU7WVF+dPHnSkGRs2rTpin3uueceY9iwYU5tMTExxv/8z//U9vLqDTNx4j3qJwEBAcZLL71U4XPk0n9VFqeGnkvnzp0z2rdvb2RkZBj9+/c3pkyZcsW+DTmnqhKn2sgprvCacPHiRW3btk2xsbGONg8PD8XGxio7O/uK486fP6/WrVurVatWV/3fcUOVnZ3tFFdJiouLqzSuDVlUVJRCQ0M1ePBgffLJJ+5eTp07e/asJKlFixZX7ENOmYuT1LDfo0pKSrR69WoVFBRc8WvnySVzcZIadi5NnjxZw4YNK5crFWnIOVWVOEk1n1MUvCZ89913KikpcXz7W5ng4OAr7qHs0KGDli1bpr/97W969dVXVVpaqj59+ujYsWN1seRrRm5uboVxzc/P148//uimVdU/oaGhWrp0qd5++229/fbbatWqlQYMGKDt27e7e2l1prS0VFOnTtUtt9zi9M2Kl7tSTll9v3MZs3FqqO9Ru3btkr+/v+x2u37/+9/r3XffVefOnSvs25BzqSpxaqi5JEmrV6/W9u3blZaWZqp/Q82pqsapNnLK7V8tbFW9e/d2+t9wnz591KlTJ/3lL3/R3Llz3bgyXIs6dOigDh06OI779OmjQ4cO6c9//rNWrlzpxpXVncmTJ2v37t36+OOP3b2Ues1snBrqe1SHDh20Y8cOnT17Vm+99Zbi4+O1adOmKxZzDVVV4tRQc+mbb77RlClTlJGR0SA/pGeWK3GqjZyi4DUhMDBQnp6eysvLc2rPy8tTSEiIqTm8vLx088036+DBg7WxxGtWSEhIhXFt2rSpfH193bSqa0OvXr0aTPGXmJiof/7zn9q8ebOuv/76SvteKafM/qxey6oSp8s1lPcob29vtWvXTpLUs2dP/fvf/9azzz6rv/zlL+X6NuRcqkqcLtdQcmnbtm06efKkevTo4WgrKSnR5s2b9fzzz6uoqEienp5OYxpiTrkSp8vVRE6xpcEEb29v9ezZU5mZmY620tJSZWZmVrqn6edKSkq0a9cuhYaG1tYyr0m9e/d2iqskZWRkmI5rQ7Zjxw7L55NhGEpMTNS7776rDRs2KDIy8qpjGmJOuRKnyzXU96jS0lIVFRVV+FxDzKUrqSxOl2souTRo0CDt2rVLO3bscDyio6N17733aseOHRUWcQ0xp1yJ0+VqJKdq9CNwFrZ69WrDbrcbL7/8srF3717jwQcfNJo3b27k5uYahmEY9913nzF9+nRH/9TUVGP9+vXGoUOHjG3bthmjR482fHx8jD179rjrFOrEuXPnjM8//9z4/PPPDUnGokWLjM8//9z4+uuvDcMwjOnTpxv33Xefo/9//vMfw8/Pz3jiiSeMffv2GYsXLzY8PT2NdevWuesU6kRV4/TnP//ZWLt2rXHgwAFj165dxpQpUwwPDw/jww8/dNcp1ImHHnrIaNasmZGVlWWcOHHC8SgsLHT0ufxn75NPPjEaNWpkLFy40Ni3b58xe/Zsw8vLy9i1a5c7TqFOuBKnhvgeNX36dGPTpk3G4cOHjZ07dxrTp083bDab8cEHHxiGQS6VqWqcGmIuXcnldx8gpyp2tTjVRk5R8FbB//7v/xo33HCD4e3tbfTq1cv49NNPHc/179/fiI+PdxxPnTrV0Tc4ONi47bbbjO3bt7th1XWr7PZZlz/KYhMfH2/079+/3JioqCjD29vbaNOmjbF8+fI6X3ddq2qc5s+fb7Rt29bw8fExWrRoYQwYMMDYsGGDexZfhyqKkSSnHLn8Z88wDOONN94wbrzxRsPb29u46aabjPfee69uF17HXIlTQ3yPuv/++43WrVsb3t7eRsuWLY1BgwY5ijjDIJfKVDVODTGXruTyQo6cqtjV4lQbOWUzDMNw/fowAAAAUL+xhxcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXACxuwIABmjp1qruXAQBuQ8ELAPXYb37zGw0dOrTC5z766CPZbDbt3LmzjlcFANcWCl4AqMcmTJigjIwMHTt2rNxzy5cvV3R0tLp16+aGlQHAtYOCFwDqsdtvv10tW7bUyy+/7NR+/vx5vfnmmxoxYoTGjBmj8PBw+fn5qWvXrnr99dcrndNms2nt2rVObc2bN3d6jW+++Ub33HOPmjdvrhYtWmj48OE6cuRIzZwUANQxCl4AqMcaNWqkcePG6eWXX5ZhGI72N998UyUlJfrd736nnj176r333tPu3bv14IMP6r777tPWrVtdfs3i4mLFxcWpSZMm+uijj/TJJ5/I399fQ4cO1cWLF2vitACgTlHwAkA9d//99+vQoUPatGmTo2358uUaOXKkWrdurccff1xRUVFq06aNHn74YQ0dOlRvvPGGy6+3Zs0alZaW6qWXXlLXrl3VqVMnLV++XEePHlVWVlYNnBEA1C0KXgCo5zp27Kg+ffpo2bJlkqSDBw/qo48+0oQJE1RSUqK5c+eqa9euatGihfz9/bV+/XodPXrU5df74osvdPDgQTVp0kT+/v7y9/dXixYtdOHCBR06dKimTgsA6kwjdy8AAHB1EyZM0MMPP6zFixdr+fLlatu2rfr376/58+fr2WefVXp6urp27arGjRtr6tSplW49sNlsTtsjpJ+2MZQ5f/68evbsqddee63c2JYtW9bcSQFAHaHgBYBrwD333KMpU6Zo1apVeuWVV/TQQw/JZrPpk08+0fDhw/W73/1OklRaWqqvvvpKnTt3vuJcLVu21IkTJxzHBw4cUGFhoeO4R48eWrNmjYKCgtS0adPaOykAqCNsaQCAa4C/v79GjRql5ORknThxQuPHj5cktW/fXhkZGdqyZYv27dun//mf/1FeXl6lcw0cOFDPP/+8Pv/8c3322Wf6/e9/Ly8vL8fz9957rwIDAzV8+HB99NFHOnz4sLKysvTII49UeHs0AKjvKHgB4BoxYcIE/fDDD4qLi1NYWJgk6cknn1SPHj0UFxenAQMGKCQkRCNGjKh0nmeeeUatWrVSv379NHbsWD3++OPy8/NzPO/n56fNmzfrhhtu0J133qlOnTppwoQJunDhAld8AVyTbMblG7kAAAAAC+EKLwAAACyNghcAAACWRsELAAAAS6PgBQAAgKVR8AIAAMDSKHgBAABgaRS8AAAAsDQKXgAAAFgaBS8AAAAsjYIXAAAAlkbBCwAAAEv7fxpA+pJjEyKNAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability of value 3 : 0.209\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Introduction to Probability for Deep Learning using Python\n",
        "\n",
        "# Probability theory is a fundamental concept in deep learning, enabling us to model uncertainty and make predictions. \n",
        "# In this code example, we'll explore the basics of probability using Python, focusing on the normal distribution and discrete distributions. \n",
        "# We'll generate random samples, visualize the distributions, calculate mean and standard deviation, and demonstrate working with discrete distributions.\n",
        "\n",
        "# Generating random numbers from the normal distribution\n",
        "num_samples = 1000\n",
        "mean = 0\n",
        "std = 1\n",
        "samples = np.random.normal(mean, std, num_samples)\n",
        "\n",
        "# Plotting the histogram of the samples\n",
        "plt.figure(figsize=(8, 4))\n",
        "plt.hist(samples, bins=30, density=True, alpha=0.5)\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Probability')\n",
        "plt.title('Normal Distribution')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Calculating the mean and standard deviation\n",
        "sample_mean = np.mean(samples)\n",
        "sample_std = np.std(samples)\n",
        "\n",
        "# Printing the calculated mean and standard deviation\n",
        "print(\"Sample Mean:\", sample_mean)\n",
        "print(\"Sample Standard Deviation:\", sample_std)\n",
        "\n",
        "# Generating random numbers from a discrete distribution\n",
        "probabilities = [0.1, 0.3, 0.2, 0.4]\n",
        "values = [1, 2, 3, 4]\n",
        "discrete_samples = np.random.choice(values, num_samples, p=probabilities)\n",
        "\n",
        "# Plotting the histogram of the discrete samples\n",
        "unique_values, value_counts = np.unique(discrete_samples, return_counts=True)\n",
        "probability_counts = value_counts / num_samples\n",
        "\n",
        "plt.figure(figsize=(8, 4))\n",
        "plt.bar(unique_values, probability_counts)\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Probability')\n",
        "plt.title('Discrete Distribution')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Calculating the probability of a specific value\n",
        "target_value = 3\n",
        "target_probability = probability_counts[np.where(unique_values == target_value)]\n",
        "print(\"Probability of value\", target_value, \":\", target_probability[0])\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "MABDzHuwpaf4"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}