{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cbe60668",
   "metadata": {},
   "source": [
    "# Probability Distribution and Cumulative Distribution\n",
    "Here we wil see few distributions and their respective CDFs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aca5931",
   "metadata": {},
   "source": [
    "#### Uniform Distribution\n",
    "Uniform distribution where the random variable x is randomly distributed say for a given intervals [a,b] and we use the notation U(a,b). \n",
    "The PDF is given as \n",
    "\n",
    "\n",
    "$$f(x)= \\frac{1}{a-b} \\text{ for $a \\le x \\le b$} $$\n",
    "\n",
    "Corresponding CDF can be given as :\n",
    "$$ F(x)  = \\int_a^x f(x) dx = \\frac{x-a}{b-a}   \\text{ for $a \\le x \\le b$} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fb950568",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.integrate import quad\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7b5eade5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDF at x=6: 0.2\n",
      "CDF at x=6: 0.8\n"
     ]
    }
   ],
   "source": [
    "## Uniform Distribution\n",
    "\n",
    "# Defining the probability density function (PDF) for the uniform distribution\n",
    "def f(x,a,b):\n",
    "    if a <= x <= b:\n",
    "        return 1/(b-a)\n",
    "    else:\n",
    "        return 0\n",
    "    \n",
    "#defining the cumulative distribution function (CDF) for the uniform distribution\n",
    "def F(x,a,b):\n",
    "    if x < a:\n",
    "        return 0\n",
    "    elif a <= x <= b:\n",
    "        return (x-a)/(b-a)\n",
    "    else:\n",
    "        return 1\n",
    "    \n",
    "# Example usage\n",
    "\n",
    "a = 2  # value of the first parameter\n",
    "b = 7  # value of the second parameter\n",
    "\n",
    "\n",
    "x=6\n",
    "print(f\"PDF at x={x}: {f(x,a,b)}\")\n",
    "print(f\"CDF at x={x}: {F(x,a,b)}\")  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee56b6ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BBx7Ayy+/LNqJ6N0uXLiAkJAQAICzszM8PT3x8MMP47PPPsPEiRPvu/zoyJEjsWvXLvXyjF5eXnj88cexePFi9RjmESNGID4+Hlu3bsWGDRtQV1eHAwcOGDw8Z/ny5Th27Biee+45qFQqDBo0CDt27ND44aqhQ4di69atePvtt/HUU0+ha9euWLJkCTIyMtTrqDdITU3FK6+8gvHjx6OyshKzZs3Cli1bdO47Pj4enTp1wurVq5Geng4nJyeMGDECy5cv11hu0JRu376tfg+dnJzg4eGBAQMGYMOGDXjmmWda/TNOZI7Y9jeNbb95tv1yuRx79uzBp59+iq1bt+Jvf/sbVCoVOnTogODgYGzatElrYvgHH3yADz74ALa2tnBxcUHXrl0xbtw4zJ07V2N5X9KPTNBn+QIiIiIiIqImcI4FEREREREZjYkFEREREREZjYkFEREREREZjYkFEREREREZjYkFEREREREZjYkFEREREREZjb9jYaC6ujpcvXoV7dq1g0wmEzscIqJWJQgCbty4AR8fn/uu0S91bP+JyJo0p/1nYmGgq1evwtfXV+wwiIhM6tKlS+jcubPYYYiK7T8RWSN92n8mFgZq164dgPoX+d6fuicikhqVSgVfX19122fN2P4TkTVpTvvPxMJADd3fLi4u/GIhIqvBoT9s/4nIOunT/lv3QFkiIiIiImoRTCyIiIiIiMhoTCyIiIiIiMhonGNBRJJXW1uL6upqscMwew4ODla/lGxL4udOP/b29rC1tRU7DCJqAUwsiEiyBEGAQqFAeXm52KFYBBsbGwQEBMDBwUHsUCwaP3fN1759e3h5eXFxACILx8SCiCSr4eSuU6dOaNOmDU9amtDwo2/FxcXw8/Pja2UEfu70JwgCKioqUFJSAgDw9vYWOSIiMgYTCyKSpNraWvXJnZubm9jhWAQPDw9cvXoVNTU1sLe3Fzsci8TPXfM5OTkBAEpKStCpUycOiyKyYKIPpl27di0CAgIgl8sRFBSErKysRuvu3r0bjz/+ODw8PODi4oKQkBDs27dPq96uXbvQp08fODo6ok+fPvjiiy+M2i8RWZ6Gse1t2rQRORLL0TAEqra2VuRI9HP48GGMGzcOPj4+kMlk+PLLL+/7nEOHDiEoKAhyuRxdu3bFunXrWjQmfu4M0/B6cU4KkWUTNbFIT09HbGwsEhISkJeXh7CwMERERKCoqEhn/cOHD+Pxxx9HRkYGcnNzMXLkSIwbNw55eXnqOjk5OYiMjMSMGTNw8uRJzJgxA1OmTMHRo0cN3i8RWS4OQ9Gfpb1Wt27dwoABA/Dhhx/qVb+goABjxoxBWFgY8vLysGjRIsyfPx+7du1q8dgs7bUUG18vImmQCYIgiLXzwYMH4+GHH0ZKSoq6rHfv3pgwYQKSkpL02kbfvn0RGRmJ119/HQAQGRkJlUqFb7/9Vl3niSeeQIcOHZCWltZi+1WpVHB1dYVSqeQvrxKZoTt37qCgoEDdM0n319RrZu5tnkwmwxdffIEJEyY0Wucf//gHvv76a+Tn56vLoqOjcfLkSeTk5Oi9r6ZeC37uDMPXjch8Naf9F22ORVVVFXJzc7Fw4UKN8vDwcGRnZ+u1jbq6Oty4cQMdO3ZUl+Xk5GDBggUa9UaPHo3k5GSj9ltZWYnKykr13yqVSq8YSdreegv45huxozDOuHFAQoLYURC1vpycHISHh2uUjR49Gqmpqaiurm50Xgnbf5KcahVwdC5w66LYkZCp+YwF+i1utc2LlliUlpaitrYWnp6eGuWenp5QKBR6beP999/HrVu3MGXKFHWZQqFocpuG7jcpKQlLly7VKy6yDoIAvP46UFcndiTGOXYMWLQI4EgE8zF79mxs3boVAGBnZwdfX19MnDgRS5cuxbVr1xAQEKCu27ZtW/j5+WHEiBGIjY1F9+7d1Y9t2bIFzz33nNb2N2zYgKioqNY/EDPT2PdDTU0NSktLG12RyJraf4VCgbfeegt79uzBlStX0KlTJzz00EOIjY3FY489hi5duuDixfqTUblcDk9PTwwaNAjR0dF49NFH1dspLCzU+Jw2eOaZZ/DJJ5+Y7HioEefWAEU7xY6CxODau1U3L/qqUPeOqxQEQa+xlmlpaUhMTMRXX32FTp06NXubzd1vfHw84uLi1H+rVCr4+vreN06Stoak4uOPAVdXcWNpLpUKePZZy0+MpOqJJ57A5s2bUV1djaysLERFReHWrVv4xz/+AQD47rvv0LdvX1RUVODUqVNYtWoVBgwYgG+++QaPPfaYejsuLi44e/asxrZdLe3D2oJ0tf26yu9mLe1/YWEhhg4divbt2+Odd95B//79UV1djX379mHevHn473//CwBYtmwZ5s6di6qqKhQWFuKTTz7BqFGj8MYbbyDhnu7Phs9pg4YVoEhkv5+o/9dnDPBgtKihkIk5t27bJVpi4e7uDltbW61egpKSEq0rSvdKT0/HnDlz8Nlnn2HUqFEaj3l5eTW5TUP36+joCEdHx/seF1mnJ54A3N3FjqJ5SkvFjoCa4ujoCC8vLwDA9OnTceDAAXz55ZfqxMLNzU39eNeuXTFu3Dg89thjmDNnDn799Vf1kp0ymUxdz9o19v1gZ2fX5NKw1tL+x8TEQCaT4ccff4Szs7O6vG/fvvjLX/6i/rtdu3bqz5Sfnx+GDRsGb29vvP7665g8eTJ69uyprnv355TMiPLn+n97PA/4RIgbC0mKaKtCOTg4ICgoCJmZmRrlmZmZCA0NbfR5aWlpmD17NrZv346xY8dqPR4SEqK1zf3796u3aeh+icjyCQJw65Y4N2OXyXBycmpyKU4bGxu8+OKLuHjxInJzc43bmUQ19v0QHBzcer/bIQhAzS1xbs340F2/fh179+7FvHnzNJKKBu3bt2/y+S+++CIEQcBXX33V3FeITK22ElCdq7/vGihuLCQ5og6FiouLw4wZMxAcHIyQkBCsX78eRUVFiI6u75aLj4/HlStXsG3bNgD1ScXMmTOxatUqDBkyRH3lycnJSd21/+KLL2LYsGFYsWIFnnrqKXz11Vf47rvv8MMPP+i9XyJ9iLeeWssTBOuYY1FRAbRtK86+b94EdJyv6eXHH3/E9u3bNYY46dKrVy8A9UNaBg0aBABQKpVoe9dBt23bVu95bObu5s2b+OWXX9R/FxQU4MSJE+jYsSP8/Py0vkOio6Px4YcfIi4uDnPnzkVOTg5SU1PVKwa2itoKYKdIH7opNwE7/T50v/zyCwRBUH+Gmqtjx47o1KkTCgsLNcpDQ0NhY/PHNcysrCwMHDjQoH1QC7lxDhBqAHtXoE1nsaMhiRE1sYiMjERZWRmWLVuG4uJiBAYGIiMjA/7+/gCA4uJijd+W+Oijj1BTU4N58+Zh3rx56vJZs2Zhy5YtAOobsR07duC1117D4sWL0a1bN6Snp2Pw4MF675eISGz//Oc/0bZtW9TU1KC6uhpPPfUUPvjgA1RUVDT6HF3zBdq1a4effvpJ/ffdJ3mW7vjx4xg5cqT674Z5EA3fCfd+hwQEBCAjIwMLFizAmjVr4OPjg9WrV2PSpEkmj93c6DPXRJ9t3Pv89PR09O79x2RRKc5NsTjlp+r/bR9oHVeUyKREn7wdExODmJgYnY81JAsNDh48qNc2J0+ejMmTJxu8X6LmssS22RJjNlabNvU9B2LtuzlGjhyJlJQU2Nvbw8fHRz1U594rwndr+H2Gu1fjsbGxwYMPPtjseC3BiBEj0NRPMd37HQIAw4cP10i0Wp1tm/qeAzHY6v+h6969O2QyGfLz85v8LZDGlJWVaa1YBtQnElL9/Fms8v/Nr+AwKGoFoicWRJZKakOhrIFMZvhwJFNzdnZu1glZXV0dVq9ejYCAAA41MScymd7DkcTUsWNHjB49GmvWrMH8+fO15lmUl5c3Oc9i1apVsLGxMSgpIRNTMrGg1sPEgojIApWVlUGhUKCiogI///wzkpOT8eOPP2LPnj3qFaGImmPt2rUIDQ3FoEGDsGzZMvTv3x81NTXIzMxESkqKukfsxo0bUCgUqK6uRkFBAT755BNs3LgRSUlJ7J2wBA09Fu2ZWFDLY2JB1AIscViRJcZMf2hYartNmzbw9/fHyJEjsX79ep7YkcECAgLw008/4a233sJLL72E4uJieHh4ICgoCCkpKep6r7/+Ol5//XU4ODjAy8sLQ4YMwffff68x34XMVPVN4FZB/X32WFArYGJBRGRmdM0NaNClS5cm5xXcbfbs2Zg9e3bLBEVWwdvbGx9++CE+/PBDnY83Ncfnbs35nJIJKc/U/yv3AuQW9uNLZBGkszwIkYlJ6TtTSsdCRESNUN61IhRRK2BiQURERGQNuCIUtTImFkQtwBLnK1hizEREZAQlJ25T62JiQURERGQN2GNBrYyJBZGBpDQvQUrHQkREOtwpBe4o6u+79hE3FpIsJhZEJGl1dXVih2AxuIpPy+Hnrnn4epmA8nT9v84BgH07cWMhyeJys0QtwBLnK1hizM3h4OAAGxsbXL16FR4eHnBwcIBM6gdtBEEQcO3aNchkMtjb24sdjsXi5655BEFAVVUVrl27BhsbGzg4OIgdknSVc0Uoan1MLIhIkmxsbBAQEIDi4mJcvXpV7HAsgkwmQ+fOnfnL3Ubg584wbdq0gZ+fH2xsOJCi1Sg5v4JaHxMLIgNJadSIlI7lbg4ODvDz80NNTQ1qa2vFDsfs2dvbM6loAfzcNY+trS3s7OzYs9PauCIUmQATCyKStIahPRzeQ6bEzx2ZFUHgilBkEuxzJGoBlnihzRJjJiIiA9y+AlQrAZkt4NJT7GhIwphYEBlIqsOHiIhIYhp6K1x6AraO4sZCksbEgoiYJBERSVnDilAcBkWtjIkFUQvgsCIiIjJbXBGKTISJBZGVYjJERGQlyrkiFJkGEwsiA0lp+JCUjoWIiO5SVwuoztTfZ48FtTImFkRERERSdfMCUHsHsHUC2nYVOxqSOCYWRC3AEocVWWLMRETUTMqGidt9ABv+ACa1LiYWRERERFLFH8YjE2JiQWQgKc1LkNKxEBHRXZScuE2mI3pisXbtWgQEBEAulyMoKAhZWVmN1i0uLsb06dPRs2dP2NjYIDY2VqvOiBEjIJPJtG5jx45V10lMTNR63MvLqzUOj4iIiEg87LEgExI1sUhPT0dsbCwSEhKQl5eHsLAwREREoKioSGf9yspKeHh4ICEhAQMGDNBZZ/fu3SguLlbffv75Z9ja2uLpp5/WqNe3b1+NeqdOnWrx4yPrYYnzFSwxZiIiaobaSuDGufr77LEgE7ATc+crV67EnDlzEBUVBQBITk7Gvn37kJKSgqSkJK36Xbp0wapVqwAAmzZt0rnNjh07avy9Y8cOtGnTRiuxsLOzYy8FERERSZfqLCDUAvbtAacHxI6GrIBoPRZVVVXIzc1FeHi4Rnl4eDiys7NbbD+pqamYOnUqnJ2dNcrPnz8PHx8fBAQEYOrUqbhw4UKT26msrIRKpdK4kXWT0rwEKR0LERH9T/n/RmO0D2Q3NZmEaIlFaWkpamtr4enpqVHu6ekJhULRIvv48ccf8fPPP6t7RBoMHjwY27Ztw759+7BhwwYoFAqEhoairKys0W0lJSXB1dVVffP19W2RGImIiIhahZLzK8i0RJ+8LbsngxYEQavMUKmpqQgMDMSgQYM0yiMiIjBp0iT069cPo0aNwp49ewAAW7dubXRb8fHxUCqV6tulS5daJEaSBku8EGSJMRMRUTOUc0UoMi3R5li4u7vD1tZWq3eipKREqxfDEBUVFdixYweWLVt237rOzs7o168fzp8/32gdR0dHODo6Gh0XSQeHDxERkVljjwWZmGg9Fg4ODggKCkJmZqZGeWZmJkJDQ43e/s6dO1FZWYlnn332vnUrKyuRn58Pb29vo/dLZImYJBERSUz1DeBWYf199liQiYi6KlRcXBxmzJiB4OBghISEYP369SgqKkJ0dDSA+uFHV65cwbZt29TPOXHiBADg5s2buHbtGk6cOAEHBwf06dNHY9upqamYMGEC3NzctPb78ssvY9y4cfDz80NJSQnefPNNqFQqzJo1q/UOliSNw4qIiMisKM/U/+vkDThqnwsRtQZRE4vIyEiUlZVh2bJlKC4uRmBgIDIyMuDv7w+g/gfx7v1Ni4EDB6rv5+bmYvv27fD390dhYaG6/Ny5c/jhhx+wf/9+nfu9fPkypk2bhtLSUnh4eGDIkCE4cuSIer9E1oDJEBGRhDWsCMVhUGRCoiYWABATE4OYmBidj23ZskWrTNBjzEaPHj2arLdjxw694yNqDIcPERGR2eL8ChKB6KtCEZH4mCQREUkMV4QiETCxIGoBHFZERERmhT0WJAImFkRWiskQEZFE3bkG3Pmt/n77vuLGQlaFiQWRgaQ0fEhKx0JEZPUaeivadgXsnMWNhawKEwsiIiIiKSnnMCgSBxMLohZgicOKLDFmIiLSg5ITt0kcTCyIiIiIpIQ9FiQSJhZEBpLSvAQpHQsRkVUTBPZYkGiYWBARERFJRcVloFoFyOyAdj3FjoasDBMLohZgifMVLDFmIl3Wrl2LgIAAyOVyBAUFISsrq8n6n376KQYMGIA2bdrA29sbzz33HMrKykwULVErKz9V/69LT8DWQdxYyOowsSAyEIcPEYkvPT0dsbGxSEhIQF5eHsLCwhAREYGioiKd9X/44QfMnDkTc+bMwenTp/HZZ5/h2LFjiIqKMnHkRK2EP4xHImJiQURMkshirVy5EnPmzEFUVBR69+6N5ORk+Pr6IiUlRWf9I0eOoEuXLpg/fz4CAgLwpz/9CX/7299w/PhxE0dO1ErKOb+CxMPEgqgFcFgRkelVVVUhNzcX4eHhGuXh4eHIzs7W+ZzQ0FBcvnwZGRkZEAQBv/32Gz7//HOMHTvWFCETtT72WJCImFgQWSkmQ2TpSktLUVtbC09PT41yT09PKBQKnc8JDQ3Fp59+isjISDg4OMDLywvt27fHBx980Oh+KisroVKpNG5EZqmuFlCeqb/fvp+4sZBVYmJBZCAOHyIyD7J7smRBELTKGpw5cwbz58/H66+/jtzcXOzduxcFBQWIjo5udPtJSUlwdXVV33x9fVs0fqIWc/NXoK4SsHUC2gaIHQ1ZISYWRMQkiSySu7s7bG1ttXonSkpKtHoxGiQlJWHo0KF45ZVX0L9/f4wePRpr167Fpk2bUFxcrPM58fHxUCqV6tulS5da/FiIWkTDilCufQEZT/HI9PipI2oBHFZEZHoODg4ICgpCZmamRnlmZiZCQ0N1PqeiogI2Nppffba2tgDqezp0cXR0hIuLi8aNyCzxh/FIZEwsiKwUkyGSgri4OGzcuBGbNm1Cfn4+FixYgKKiIvXQpvj4eMycOVNdf9y4cdi9ezdSUlJw4cIF/Pvf/8b8+fMxaNAg+Pj4iHUYRC2jnBO3SVx2YgdAZKk4fIhIfJGRkSgrK8OyZctQXFyMwMBAZGRkwN/fHwBQXFys8ZsWs2fPxo0bN/Dhhx/ipZdeQvv27fHoo49ixYoVYh0CUcvhilAkMpnQWN8vNUmlUsHV1RVKpZLd4lbq99+Bjh3r71dVAfb24sbTXNXVgMP/fpT1+nWgQwdx4yHzxjbvD3wtyCzV3gF2tgWEWmDCFaANe+CoZTSnzeNQKKIWwGFFREQkKtXZ+qTCoQPg5C12NGSlmFgQWSkmQ0REEqJeESqQDTyJhokFkYGkNIhQSsdCRGSVuCIUmQHRE4u1a9ciICAAcrkcQUFByMrKarRucXExpk+fjp49e8LGxgaxsbFadbZs2QKZTKZ1u3PnjsH7JSIiIjJrXBGKzICoiUV6ejpiY2ORkJCAvLw8hIWFISIiQmMFj7tVVlbCw8MDCQkJGDBgQKPbdXFxQXFxscZNLpcbvF+i+7HEXmdLjJmIiBrBHgsyA6ImFitXrsScOXMQFRWF3r17Izk5Gb6+vkhJSdFZv0uXLli1ahVmzpwJV1fXRrcrk8ng5eWlcTNmv0S6cPgQERGZhWoVcOti/X32WJCIREssqqqqkJubi/DwcI3y8PBwZGdnG7Xtmzdvwt/fH507d8aTTz6JvLw8k+yXyFIxSSIismDlp+v/dfIBHDuKGwtZNdESi9LSUtTW1sLT01Oj3NPTEwqFwuDt9urVC1u2bMHXX3+NtLQ0yOVyDB06FOfPnzdqv5WVlVCpVBo3ogYcVkRERKLhD+ORmRB98rbsnjMyQRC0yppjyJAhePbZZzFgwACEhYVh586d6NGjBz744AOj9puUlARXV1f1zdfX1+AYicwBkyEiIoko5/wKMg+iJRbu7u6wtbXV6iUoKSnR6k0who2NDR555BF1j4Wh+42Pj4dSqVTfLl261GIxkmXi8CEiIjIL7LEgMyFaYuHg4ICgoCBkZmZqlGdmZiI0NLTF9iMIAk6cOAFvb2+j9uvo6AgXFxeNG5FUMEkiIrJg6hWh+okbB1k9OzF3HhcXhxkzZiA4OBghISFYv349ioqKEB0dDaC+l+DKlSvYtm2b+jknTpwAUD9B+9q1azhx4gQcHBzQp08fAMDSpUsxZMgQdO/eHSqVCqtXr8aJEyewZs0avfdL1FwcVkRERKK4U1J/gwxw7S12NGTlRE0sIiMjUVZWhmXLlqG4uBiBgYHIyMiAv78/gPofxLv3tyUGDhyovp+bm4vt27fD398fhYWFAIDy8nL89a9/hUKhgKurKwYOHIjDhw9j0KBBeu+XyBowGSIikoCG+RVtuwJ2zuLGQlZPJggcBGEIlUoFV1dXKJVKDouyUteuAZ061d+vq7O8E3VBAGz+Nxjy2jXA3V3ceMi8sc37A18LMitnVwO5LwKdnwKGfSl2NCRBzWnzRF8ViojEx8sLREQWqpwTt8l8MLEgagGW1ltBREQSwRWhyIwwsSCyUkyGiIgsnCDc9RsWXBGKxMfEgshAHD5ERESiqrgE1NwAbOyBdt3FjoaIiQURMUkiIrJI5afq/23XE7B1EDcWIjCxICIiIrJM6h/G4/wKMg9MLIgMxKv8REQkKq4IRWaGiQURMUkiIrJE7LEgM8PEgshIXF2JiIhMrq4GUObX3+eKUGQmmFgQWTEmRUREFurGL0BdJWDbBnDuInY0RACYWBAZjMOHiIhINOofxusLyHg6R+aBn0QiYpJERGRpyjm/gswPEwsiI3E4ERERmZySK0KR+WFiQWTFmBQREVko9YpQnLhN5oOJBZGBOHyIiIhEUXsHuHG+/j6HQpEZYWJBREySiIgsiTIfEOoAh46A3EvsaIjUmFgQGYnDiYiIyKTu/mE8fgmRGWFiQWTF+H1ERGSByjlxm8wTEwsiA3H4EBERiULJpWbJPDGxICImSURElkTdY8EVoci8MLEgMhKHExERkclUq4CKovr77fuKGwvRPZhYEBlIClf5mRQREVmYht4KpwcAhw7ixkJ0DyYWRERERJaC8yvIjDGxIDKSFK76S6H3hYjIKnBFKDJjoicWa9euRUBAAORyOYKCgpCVldVo3eLiYkyfPh09e/aEjY0NYmNjteps2LABYWFh6NChAzp06IBRo0bhxx9/1KiTmJgImUymcfPy4g/MEBERkZljjwWZMVETi/T0dMTGxiIhIQF5eXkICwtDREQEioqKdNavrKyEh4cHEhISMGDAAJ11Dh48iGnTpuHAgQPIycmBn58fwsPDceXKFY16ffv2RXFxsfp26tSpFj8+kjYpXOWXQm8LEZFVaeixaM8Vocj8iJpYrFy5EnPmzEFUVBR69+6N5ORk+Pr6IiUlRWf9Ll26YNWqVZg5cyZcXV111vn0008RExODhx56CL169cKGDRtQV1eH77//XqOenZ0dvLy81DcPD48WPz4iSyGFJImISPLulACV1wDIAJfeYkdDpEW0xKKqqgq5ubkIDw/XKA8PD0d2dnaL7aeiogLV1dXo2LGjRvn58+fh4+ODgIAATJ06FRcuXGixfZJ14VV/IiIyifL/ja5o2w2wayNuLEQ62Im149LSUtTW1sLT01Oj3NPTEwqFosX2s3DhQjzwwAMYNWqUumzw4MHYtm0bevTogd9++w1vvvkmQkNDcfr0abi5uencTmVlJSorK9V/q1SqFouRSCxMioiILEg551eQeRN98rbsnjMbQRC0ygz1zjvvIC0tDbt374ZcLleXR0REYNKkSejXrx9GjRqFPXv2AAC2bt3a6LaSkpLg6uqqvvn6+rZIjGS5OHyIiIhMSskVoci8iZZYuLu7w9bWVqt3oqSkRKsXwxDvvfceli9fjv3796N///5N1nV2dka/fv1w/vz5RuvEx8dDqVSqb5cuXTI6RiJzwSSJiMgCcOI2mTnREgsHBwcEBQUhMzNTozwzMxOhoaFGbfvdd9/FG2+8gb179yI4OPi+9SsrK5Gfnw9vb+9G6zg6OsLFxUXjRgRwOBGR2JqzbDlQ3+YnJCTA398fjo6O6NatGzZt2mSiaIkMJAhcapbMnmhzLAAgLi4OM2bMQHBwMEJCQrB+/XoUFRUhOjoaQH0vwZUrV7Bt2zb1c06cOAEAuHnzJq5du4YTJ07AwcEBffr0AVA//Gnx4sXYvn07unTpou4Radu2Ldq2bQsAePnllzFu3Dj4+fmhpKQEb775JlQqFWbNmmXCoycSH5MisnQNy5avXbsWQ4cOxUcffYSIiAicOXMGfn5+Op8zZcoU/Pbbb0hNTcWDDz6IkpIS1NTUmDhyoma6dRGouQnY2APtuosdDZFOoiYWkZGRKCsrw7Jly1BcXIzAwEBkZGTA398fQP0P4t37mxYDBw5U38/NzcX27dvh7++PwsJCAPVXrqqqqjB58mSN5y1ZsgSJiYkAgMuXL2PatGkoLS2Fh4cHhgwZgiNHjqj3S6QPDh8iEt/dy5YDQHJyMvbt24eUlBQkJSVp1d+7dy8OHTqECxcuqFcL7NKliylDJjJMQ2+FS6/65ILIDImaWABATEwMYmJidD62ZcsWrTLhPmdzDQlGU3bs2KFPaERWg0kSWaKGZcsXLlyoUd7UsuVff/01goOD8c477+Djjz+Gs7Mzxo8fjzfeeANOTk6mCJvIMOWcuE3mT/TEgsjScTgRkTgMWbb8woUL+OGHHyCXy/HFF1+gtLQUMTExuH79eqPzLLjcOJkFzq8gCyD6crNElkoKV/mZFJEUNGfZ8rq6OshkMnz66acYNGgQxowZg5UrV2LLli24ffu2zudwuXEyC+oeC64IReaLiQUREVkkQ5Yt9/b2xgMPPABXV1d1We/evSEIAi5fvqzzOVxunERXVwOo8uvvs8eCzBgTCyIjSeGqvxR6X8j6GLJs+dChQ3H16lXcvHlTXXbu3DnY2Nigc+fOOp/D5cZJdDfOA3VVgJ0z4MyFZsh8MbEgIiKLFRcXh40bN2LTpk3Iz8/HggULtJYtnzlzprr+9OnT4ebmhueeew5nzpzB4cOH8corr+Avf/kLJ2+T+VL/4nZfQMZTNzJfnLxNZCApXOWXQm8LWbfmLlvetm1bZGZm4oUXXkBwcDDc3NwwZcoUvPnmm2IdAtH9cUUoshBMLIiIyKI1d9nyXr16aQ2fIjJrXBGKLAT704iMJIWr/lLofSEikqyGHov2XBGKzBsTCyIiIiJzVXMbuPlL/X0OhSIzx8SCyEBSuMovhd4WIiJJU+UDQh3g6AbIdS+jTGQumFgQkSSSJCIiSbp74javBpGZY2JBZCS280RE1GqUXBGKLAcTCyIrxqSIiMjMceI2WRAmFkQG4vAhIiJqdVxqliwIEwsiYpJERGSOqsqBikv19137ihoKkT6YWBAZicOJiIioVShP1//bpjPg0F7UUIj0wcSCyEBSuMrPpIiIyIyVc+I2WRYmFkRERETmiPMryMIwsSAykhSu+kuh94WISHLUPRZcEYosg53YARARkXU5e/Ys0tLSkJWVhcLCQlRUVMDDwwMDBw7E6NGjMWnSJDg6OoodJpG4BAFQnqq/zx4LshDN7rE4e/YsEhMT8dhjj6Fbt27w9vZG//79MWvWLGzfvh2VlZWtESeR2ZHCVX4p9LaQ5cjLy8Pjjz+OAQMG4PDhw3jkkUcQGxuLN954A88++ywEQUBCQgJ8fHywYsUKfp+QdbvzG1BZBkAGuPQWOxoivejdY5GXl4dXX30VWVlZCA0NxaBBgzBhwgQ4OTnh+vXr+Pnnn5GQkIAXXngBr776KmJjY3nFiYiI1CZMmIBXXnkF6enp6NixY6P1cnJy8H//9394//33sWjRIhNGSGRGGuZXtHsQsHMSNxYiPemdWPALgUg3KVz1l0LvC5m/8+fPw8HB4b71QkJCEBISgqqqKhNERWSmuCIUWSC9Ewt+IRARkTH0+Q4BgIqKCrRp00bv+kSSpF4RihO3yXLoPceiOV8Izam/du1aBAQEQC6XIygoCFlZWY3WLS4uxvTp09GzZ0/Y2NggNjZWZ71du3ahT58+cHR0RJ8+ffDFF18YtV8iXaRwlV8KvS1kmUaMGIHLly9rlR89ehQPPfSQ6QMiMjflXGqWLI9By8221BdCeno6YmNjkZCQgLy8PISFhSEiIgJFRUU661dWVsLDwwMJCQkYMGCAzjo5OTmIjIzEjBkzcPLkScyYMQNTpkzB0aNHDd4vERG1LBcXF/Tv3x87duwAANTV1SExMRHDhg3D+PHjRY6OSGRC3R+/us2hUGRJBAOMGzdO6NChg5CWliYIgiDU1tYKS5YsERwcHISXXnpJ7+0MGjRIiI6O1ijr1auXsHDhwvs+d/jw4cKLL76oVT5lyhThiSee0CgbPXq0MHXq1BbZbwOlUikAEJRKpd7PIWk5d04QAEFwdRU7EsO5uNQfw7lzYkdC5q412ryUlBTB2dlZmDZtmhASEiI88MADQmZmZottv7Ww/adWd+OCIHwKQUhzEITaKrGjISvXnDbPoN+x+Prrr7Fu3TpERUXh66+/RmFhIYqKirBnzx6MGjVKr21UVVUhNzcXCxcu1CgPDw9Hdna2IWEBqO+xWLBggUbZ6NGjkZyc3Kr7JSKi5omOjsbFixexYsUK2NnZ4eDBgwgNDRU7LCLxNQyDcukF2NiLGwtRMxj8A3nGfiGUlpaitrYWnp6eGuWenp5QKBSGhgWFQtHkNg3db2Vlpcaa6iqVyuAYSRo4x4LIcL///juioqLw/fff46OPPsKhQ4cQHh6Od955BzExMWKHRyQuJVeEIstk0ByL33//HZMmTUJKSgo++ugjTJkyBeHh4Vi7dm2ztyW758xGEAStstbYZnP3m5SUBFdXV/XN19fXqBiJzIkUkiSyLIGBgfjtt9+Ql5eHuXPn4pNPPkFqaioWL16MsWPHih0ekbjKuSIUWSaDEouW+EJwd3eHra2tVi9BSUmJVm9Cc3h5eTW5TUP3Gx8fD6VSqb5dunTJ4BhJWnjVn6j5oqOjcfjwYQQEBKjLIiMjcfLkSS5XTqTkilBkmQxKLFriC8HBwQFBQUHIzMzUKM/MzDRqjG1ISIjWNvfv36/epqH7dXR0hIuLi8aNrJsUrvIzKSKxLF68GDY22l9BnTt31mqfiaxKXTWg+m/9fQ6FIgtj0ByLxYsX6yxv7hdCXFwcZsyYgeDgYISEhGD9+vUoKipCdHQ0gPpegitXrmDbtm3q55w4cQIAcPPmTVy7dg0nTpyAg4MD+vTpAwB48cUXMWzYMKxYsQJPPfUUvvrqK3z33Xf44Ycf9N4vERG1vKKiIvj5+eld/8qVK3jggQdaMSIiM3TjPFBXBdi1BZz1//9CZA70Tixa4wshMjISZWVlWLZsGYqLixEYGIiMjAz4+/sDqP9BvHt/W2LgwIHq+7m5udi+fTv8/f1RWFgIAAgNDcWOHTvw2muvYfHixejWrRvS09MxePBgvfdL1BxSuOovhd4XMn+PPPIIxo8fj7lz52LQoEE66yiVSuzcuROrVq3C3/72N7zwwgsmjpJIZA3zK1z7AjKDBpYQiUYmCPqdUnh6evIL4S4qlQqurq5QKpUcFmWlzp4FevUCOnQArl8XOxrDdOgAlJcD//0v0LOn2NGQOWuJNu/69etYvnw5Nm3aBHt7ewQHB8PHxwdyuRy///47zpw5g9OnTyM4OBivvfYaIiIiWvgoWgbbf2pV/3kd+PkNoNscYPBGsaMhalabp3ePRX5+PpYvX44nnnjivl8I7777rtl+IRC1FClc5ZdCbwtZjo4dO+K9997Dm2++iYyMDGRlZaGwsBC3b9+Gu7s7nnnmGYwePRqBgRxXTlZM3WPBFaHI8uidWFy+fBkrVqzAm2++iW+//RaHDx/mFwIRETXLhQsXEBAQgIkTJ2LixIlih0NkfrgiFFkwvROLgQMHQqFQwMPDAy+99BKOHTsGNze31oyNyCJI4aq/FHpfyDJ0794dxcXF6NSpE4D6OW+rV682aplxIsmoqQBu/FJ/nytCkQXSe1ZQ+/btceHCBQBAYWEh6urqWi0oIiKSpnun9WVkZODWrVsiRUNkZlT5AATA0R2QdxI7GqJm07vHYtKkSRg+fDi8vb0hk8kQHBwMW1tbnXUbEhAiKZPCVX4p9LYQEUmGen5FIBtoskh6Jxbr16/HxIkT8csvv2D+/PmYO3cu2rVr15qxERGRxMhkMsjuOWG6928iq6WeX8GJ22SZmvUDeU888QSA+t+PePHFF5lYEEEaF5Wk0PtClkEQBMyePRuOjo4AgDt37iA6OhrOzs4a9Xbv3i1GeETiKufEbbJsBv3y9ubNm1s6DiIisgKzZs3S+PvZZ58VKRIiM6S8aygUkQUyKLEgImlc5ZdCbwtZFl6YImpE1e9AxeX6+659xY2FyED8rXgiIiIisZWfrv+3jS/g4CpuLEQGYmJBZCQpXPWXQu8LEZFF4zAokgAmFkQG4sk4ERG1mHKuCEWWj4kFkRWTQm8LEZEkKLkiFFk+JhZERpLCyTl7X4iIRCQIHApFksDEgoiIiEhMdxRAZRkgswFceokdDZHBmFgQGUgKV/ml0NtCRGTxGuZXtH0QsHMSNxYiIzCxICIiIhIT51eQRDCxIDKSFK76S6H3hazX2rVrERAQALlcjqCgIGRlZen1vH//+9+ws7PDQw891LoBEt1PQ4+FK1eEIsvGxIKIiCxWeno6YmNjkZCQgLy8PISFhSEiIgJFRUVNPk+pVGLmzJl47LHHTBQpURPYY0ESwcSCyEBSuMovhd4Wsm4rV67EnDlzEBUVhd69eyM5ORm+vr5ISUlp8nl/+9vfMH36dISEhJgoUqJGCHWA8n+/us0VocjCMbEgIiKLVFVVhdzcXISHh2uUh4eHIzs7u9Hnbd68Gb/++iuWLFmi134qKyuhUqk0bkQt5lYhUHMLsHEA2j0odjRERmFiQWQkKVz1l0LvC1mf0tJS1NbWwtPTU6Pc09MTCoVC53POnz+PhQsX4tNPP4WdnZ1e+0lKSoKrq6v65uvra3TsRGoN8ytcegM2+n0micwVEwsiIrJosnuye0EQtMoAoLa2FtOnT8fSpUvRo0cPvbcfHx8PpVKpvl26dMnomInU1PMrOHGbLB9TYyIDSeEqvxR6W8h6ubu7w9bWVqt3oqSkRKsXAwBu3LiB48ePIy8vD88//zwAoK6uDoIgwM7ODvv378ejjz6q9TxHR0c4Ojq2zkEQlXPiNkmH6D0WzV0m8NChQwgKCoJcLkfXrl2xbt06jcdHjBgBmUymdRs7dqy6TmJiotbjXl5erXJ8RETUOhwcHBAUFITMzEyN8szMTISGhmrVd3FxwalTp3DixAn1LTo6Gj179sSJEycwePBgU4VO9IeGHgtO3CYJELXHomGZwLVr12Lo0KH46KOPEBERgTNnzsDPz0+rfkFBAcaMGYO5c+fik08+wb///W/ExMTAw8MDkyZNAgDs3r0bVVVV6ueUlZVhwIABePrppzW21bdvX3z33Xfqv21tbVvpKEnqpHDVXwq9L2Sd4uLiMGPGDAQHByMkJATr169HUVERoqOjAdQPY7py5Qq2bdsGGxsbBAZqnrx16tQJcrlcq5zIJOqqAdV/6++zx4IkQNTE4u5lAgEgOTkZ+/btQ0pKCpKSkrTqr1u3Dn5+fkhOTgYA9O7dG8ePH8d7772nTiw6duyo8ZwdO3agTZs2WomFnZ0deynIKDwZJxJfZGQkysrKsGzZMhQXFyMwMBAZGRnw9/cHABQXF9/3Ny2IRKM6V59c2LUF2mhfUCWyNKINhTJkmcCcnByt+qNHj8bx48dRXV2t8zmpqamYOnUqnJ2dNcrPnz8PHx8fBAQEYOrUqbhw4UKT8XK5QZIiKfS2EMXExKCwsBCVlZXIzc3FsGHD1I9t2bIFBw8ebPS5iYmJOHHiROsHSaTL3cOg2CCTBIiWWBiyTKBCodBZv6amBqWlpVr1f/zxR/z888/qHpEGgwcPxrZt27Bv3z5s2LABCoUCoaGhKCsrazReLjdIjeF3ARERGaScK0KRtIg+eVvfZQKbqq+rHKjvrQgMDMSgQYM0yiMiIjBp0iT069cPo0aNwp49ewAAW7dubXS/XG6QpIzDuoiIRKDkilAkLaLNsWjuMoEA4OXlpbO+nZ0d3NzcNMorKiqwY8cOLFu27L6xODs7o1+/fjh//nyjdbjcIN2LJ+NERGSUcq4IRdIiWo9Fc5cJBICQkBCt+vv370dwcDDs7e01ynfu3InKyko8++yz942lsrIS+fn58Pb2buZREFk2DuMiIhJJzS3g5q/199ljQRIh6lCouLg4bNy4EZs2bUJ+fj4WLFigtUzgzJkz1fWjo6Nx8eJFxMXFIT8/H5s2bUJqaipefvllrW2npqZiwoQJWj0ZAPDyyy/j0KFDKCgowNGjRzF58mSoVCrMmjWr9Q6WJEsKJ+fsfSEiMjFlPgABcPQA5J3EjoaoRYi63GxzlwkMCAhARkYGFixYgDVr1sDHxwerV69WLzXb4Ny5c/jhhx+wf/9+nfu9fPkypk2bhtLSUnh4eGDIkCE4cuSIer9ERERErYrzK0iCRE0sgPplAmNiYnQ+tmXLFq2y4cOH46effmpymz169FBP6tZlx44dzYqRSBcpXOWXQm8LEZFFUs+v4IpQJB2irwpFREREZHXYY0ESxMSCyEhSuOovhd4XIiKLwhWhSIKYWBARERGZUtXvwO0r9ffb9xU3FqIWxMSCyEBSuMovhd4WIiKL09Bb0cYPsHcRNxaiFsTEgoiIiMiU1PMrOHGbpIWJBZGRpHDVXwq9L0REFqOcE7dJmphYEBmIJ+NERGQQJSdukzQxsSCyYlLobSEisiiCAJSfqr/PHguSGCYWREbiyTkREentdnH9qlAyG8Cll9jRELUoJhZExGFdRESm0jAMql13wFYubixELYyJBZGBeDJORETNpv5hPK4IRdLDxILIinEYFxGRiSm5IhRJFxMLIiPx5JyIiPRWzhWhSLqYWBARh3UREZmCUAcoT9ffZ48FSRATCyID8WSciIia5WYBUFsB2DgCbbuJHQ1Ri2NiQWTFOIyLiMiE1D+M1wewsRM3FqJWwMSCyEhSODln7wsRkQlwfgVJHBMLIiIiIlPgilAkcUwsiAwkhav8UuhtISKyGOyxIIljYkFERETU2mqrANV/6++zx4IkiokFkZGkcNVfCr0vRERm7cY5QKgB7F2ANr5iR0PUKphYEBmIJ+NERKS3u4dBSeGKFJEOTCyIrBi/24iITIQTt8kKMLEgMhJPzomI6L6UnLhN0id6YrF27VoEBARALpcjKCgIWVlZTdY/dOgQgoKCIJfL0bVrV6xbt07j8S1btkAmk2nd7ty5Y9R+iaSMw7qIiFpZOXssSPpETSzS09MRGxuLhIQE5OXlISwsDBERESgqKtJZv6CgAGPGjEFYWBjy8vKwaNEizJ8/H7t27dKo5+LiguLiYo2bXC43eL9EuvBknIiI9FJzC7h5of4+eyxIwkRNLFauXIk5c+YgKioKvXv3RnJyMnx9fZGSkqKz/rp16+Dn54fk5GT07t0bUVFR+Mtf/oL33ntPo55MJoOXl5fGzZj9EkkVh3EREZmA8gwAAZB3AuQeYkdD1GpESyyqqqqQm5uL8PBwjfLw8HBkZ2frfE5OTo5W/dGjR+P48eOorq5Wl928eRP+/v7o3LkznnzySeTl5Rm1XwCorKyESqXSuBEBPDknIqL7UK8I1U/cOIhamWiJRWlpKWpra+Hp6alR7unpCYVCofM5CoVCZ/2amhqUlpYCAHr16oUtW7bg66+/RlpaGuRyOYYOHYrz588bvF8ASEpKgqurq/rm68s1qEk6OKyLiKgVcUUoshKiT96W3XO5VxAErbL71b+7fMiQIXj22WcxYMAAhIWFYefOnejRowc++OADo/YbHx8PpVKpvl26dOn+B0eSxpNxIiLSSzlXhCLrYCfWjt3d3WFra6vVS1BSUqLVm9DAy8tLZ307Ozu4ubnpfI6NjQ0eeeQRdY+FIfsFAEdHRzg6Ot73uIgsCYdxERGZgPJU/b/ssSCJE63HwsHBAUFBQcjMzNQoz8zMRGhoqM7nhISEaNXfv38/goODYW9vr/M5giDgxIkT8Pb2Nni/RE3hyTkRETWqsgy4XVx/37WvuLEQtTLReiwAIC4uDjNmzEBwcDBCQkKwfv16FBUVITo6GkD98KMrV65g27ZtAIDo6Gh8+OGHiIuLw9y5c5GTk4PU1FSkpaWpt7l06VIMGTIE3bt3h0qlwurVq3HixAmsWbNG7/0SWRsO6yIiaiXK0/X/OncB7NuJGgpRaxM1sYiMjERZWRmWLVuG4uJiBAYGIiMjA/7+/gCA4uJijd+WCAgIQEZGBhYsWIA1a9bAx8cHq1evxqRJk9R1ysvL8de//hUKhQKurq4YOHAgDh8+jEGDBum9XyJ98GSciIjui/MryIrIBIGnR4ZQqVRwdXWFUqmEi4uL2OGQCLKzgaFDgW7dgF9+ETsawzz4IPDrr/XHEhIidjRkztjm/YGvBTXLsRjgfArQZyHwUJLY0RA1W3PaPNFXhSKydFKYY8HLC0RErYQ9FmRFmFgQGYgn40RE1CRBAMq5IhRZDyYWRFZMCr0tRERm6/ZVoLockNkCLr3Ejoao1TGxIDIST86JxLV27VoEBARALpcjKCgIWVlZjdbdvXs3Hn/8cXh4eMDFxQUhISHYt2+fCaMlq9IwDKpdD8CWv4VF0sfEgog4rIssVnp6OmJjY5GQkIC8vDyEhYUhIiJCY0XBux0+fBiPP/44MjIykJubi5EjR2LcuHHIy8szceRkFZT/Syw4DIqsBBMLIgPxZJxIfCtXrsScOXMQFRWF3r17Izk5Gb6+vkhJSdFZPzk5Ga+++ioeeeQRdO/eHcuXL0f37t3xzTffmDhysgpKTtwm68LEgsiKcRgXWbKqqirk5uYiPDxcozw8PBzZ2dl6baOurg43btxAx44dG61TWVkJlUqlcSPSSzl7LMi6MLEgMhJPzonEUVpaitraWnh6emqUe3p6QqFQ6LWN999/H7du3cKUKVMarZOUlARXV1f1zdfX16i4yUrU1f7xq9vssSArwcSCiDisiyya7J7sXhAErTJd0tLSkJiYiPT0dHTq1KnRevHx8VAqlerbpUuXjI6ZrMCtAqD2NmArB9p2EzsaIpOwEzsAIkvFk3Eicbm7u8PW1lard6KkpESrF+Ne6enpmDNnDj777DOMGjWqybqOjo5wdOSKPtRMDcOgXPoANrbixkJkIuyxILJiHMZFlszBwQFBQUHIzMzUKM/MzERoaGijz0tLS8Ps2bOxfft2jB07trXDJGvFFaHICrHHgshIPDknEk9cXBxmzJiB4OBghISEYP369SgqKkJ0dDSA+mFMV65cwbZt2wDUJxUzZ87EqlWrMGTIEHVvh5OTE1xdXUU7DpKgcq4IRdaHiQURcVgXWazIyEiUlZVh2bJlKC4uRmBgIDIyMuDv7w8AKC4u1vhNi48++gg1NTWYN28e5s2bpy6fNWsWtmzZYurwScqUp+r/ZY8FWREmFkQG4sk4kXmIiYlBTEyMzsfuTRYOHjzY+gER1VYCqnP199ljQVaEcyyIrBiHcRERtYIb5wChBrB3Bdp0FjsaIpNhYkFkJJ6cExGRhrt/GI9fEmRFmFgQGUhKQ6GkdCxERKJTcuI2WScmFkREREQtiStCkZViYkFkJEvu5bbk2ImIzFY5V4Qi68TEgog4FIqIqKVU3wRuFdTfZ48FWRkmFkQG4sk4ERFpUZ6p/1fuBcjdxY2FyMSYWBBZMQ6FIiJqYcq7VoQisjJMLIiMxJNzIiJS48RtsmKiJxZr165FQEAA5HI5goKCkJWV1WT9Q4cOISgoCHK5HF27dsW6des0Ht+wYQPCwsLQoUMHdOjQAaNGjcKPP/6oUScxMREymUzj5uXl1eLHRmQpOKyLiKiFsMeCrJioiUV6ejpiY2ORkJCAvLw8hIWFISIiAkVFRTrrFxQUYMyYMQgLC0NeXh4WLVqE+fPnY9euXeo6Bw8exLRp03DgwAHk5OTAz88P4eHhuHLlisa2+vbti+LiYvXt1KlTrXqsJD08GSciIi0NK0Kxx4KskJ2YO1+5ciXmzJmDqKgoAEBycjL27duHlJQUJCUladVft24d/Pz8kJycDADo3bs3jh8/jvfeew+TJk0CAHz66acaz9mwYQM+//xzfP/995g5c6a63M7Ojr0UZPU4jIuIqAXdKQXuKOrvu/YRNxYiEYjWY1FVVYXc3FyEh4drlIeHhyM7O1vnc3JycrTqjx49GsePH0d1dbXO51RUVKC6uhodO3bUKD9//jx8fHwQEBCAqVOn4sKFC0YcDVkznpwTEREAQHm6/l/nAMC+nbixEIlAtMSitLQUtbW18PT01Cj39PSEQqHQ+RyFQqGzfk1NDUpLS3U+Z+HChXjggQcwatQoddngwYOxbds27Nu3Dxs2bIBCoUBoaCjKysoajbeyshIqlUrjRiQVHNZFRNQCOL+CrJzok7dl91zuFQRBq+x+9XWVA8A777yDtLQ07N69G3K5XF0eERGBSZMmoV+/fhg1ahT27NkDANi6dWuj+01KSoKrq6v65uvre/+DI0njyTgREWngilBk5URLLNzd3WFra6vVO1FSUqLVK9HAy8tLZ307Ozu4ublplL/33ntYvnw59u/fj/79+zcZi7OzM/r164fz5883Wic+Ph5KpVJ9u3TpUpPbJLIEHMZFRNSC2GNBVk60xMLBwQFBQUHIzMzUKM/MzERoaKjO54SEhGjV379/P4KDg2Fvb68ue/fdd/HGG29g7969CA4Ovm8slZWVyM/Ph7e3d6N1HB0d4eLionEjAnhyTkREqO/G5opQZOVEHQoVFxeHjRs3YtOmTcjPz8eCBQtQVFSE6OhoAPW9BHev5BQdHY2LFy8iLi4O+fn52LRpE1JTU/Hyyy+r67zzzjt47bXXsGnTJnTp0gUKhQIKhQI3b95U13n55Zdx6NAhFBQU4OjRo5g8eTJUKhVmzZpluoMniyeloVBSOhYiIlHcvgJUKwGZHeDSS+xoiEQh6nKzkZGRKCsrw7Jly1BcXIzAwEBkZGTA398fAFBcXKzxmxYBAQHIyMjAggULsGbNGvj4+GD16tXqpWaB+h/cq6qqwuTJkzX2tWTJEiQmJgIALl++jGnTpqG0tBQeHh4YMmQIjhw5ot4vERERUbM0zK9w6QHYOogbC5FIRE0sACAmJgYxMTE6H9uyZYtW2fDhw/HTTz81ur3CwsL77nPHjh36hkd0X5Y8FMqSYyciMitKTtwmEn1VKCIiIiKLxxWhiJhYEBlKSvMSpHQsRESiaJi4zRWhyIoxsSAiIiIyRl0toDpTf589FmTFmFgQGcmS5ylYcuxERGbj5gWg9g5g6wS07Sp2NESiYWJBRBwKRURkDPXE7T6Aja24sRCJiIkFkYF4Mk5ERAA4cZvof5hYEFkxDoUiImoBDT0WnLhNVo6JBZGReHJORGTlGlaEYo8FWTkmFkTEYV1ERIaqrQRunKu/zx4LsnJMLIgMxJNxIiKC6iwg1AL27QGnB8SOhkhUTCyIrBiHcRERGenu+RVsVMnKMbEgMhK/R4iIrBhXhCJSY2JBZCApDYWS0rEQEZkUV4QiUmNiQURERGQorghFpMbEgshIljwUypJjJyISXfUN4FZh/X32WBAxsSAiIiIyiPJM/b9O3oCjm7ixEJkBJhZEBpLSvAQpHQsRkckoOXGb6G5MLIiIiIgMwRWhiDQwsSAykiXPU7Dk2ImIRNcwcZvzK4gAMLEgIiIiMgyHQhFpYGJBZCApzUuQ0rEQEZnEnWvAnd/q77fvK24sRGaCiQURERFRcylP1//btitg5yxuLERmgokFkZEseZ6CJcdORCQqTtwm0sLEgog4FIqIqLka5ldw4jaRmuiJxdq1axEQEAC5XI6goCBkZWU1Wf/QoUMICgqCXC5H165dsW7dOq06u3btQp8+feDo6Ig+ffrgiy++MHq/RPfiyTiReWiN7xGi+2pYEYo9FkRqoiYW6enpiI2NRUJCAvLy8hAWFoaIiAgUFRXprF9QUIAxY8YgLCwMeXl5WLRoEebPn49du3ap6+Tk5CAyMhIzZszAyZMnMWPGDEyZMgVHjx41eL9EUsWhUGTpWuN7hOi+BOGuHot+4sZCZEZkgiDeddfBgwfj4YcfRkpKirqsd+/emDBhApKSkrTq/+Mf/8DXX3+N/Px8dVl0dDROnjyJnJwcAEBkZCRUKhW+/fZbdZ0nnngCHTp0QFpamkH71UWlUsHV1RVKpRIuLi7NO3CShIwMYOxYIDgYOHZM7GgMExwM5ObWH0tEhNjRkDkz1zavNb5H7sdcXwsyoVuXgK/8AJkdMOUWYOsgdkREraY5bZ6diWLSUlVVhdzcXCxcuFCjPDw8HNnZ2Tqfk5OTg/DwcI2y0aNHIzU1FdXV1bC3t0dOTg4WLFigVSc5Odng/bakoiKgoKDVd0MmcOqU2BG0nP/8B2jTRuwoyJSGDxc7AuO11vdIqyn9Eai93XrbJ9O5mlH/r0tPJhVEdxEtsSgtLUVtbS08PT01yj09PaFQKHQ+R6FQ6KxfU1OD0tJSeHt7N1qnYZuG7BcAKisrUVlZqf5bpVLd/yB12L4diI836KlkpmxEn6lkuIbY7zkvIysghTlCrfU9cq+Wav9xZCagOmvYc8k8uQ0WOwIisyJaYtFAds8gb0EQtMruV//ecn222dz9JiUlYenSpY0+ri83N6B3b6M3Q2bC1haYN0/sKAz3/PPAu+8CtbViR0JkuNb4HrlbS7X/aNsNZrBmCrUUe1egD6/KEN1NtMTC3d0dtra2WleVSkpKtK4mNfDy8tJZ387ODm5ubk3WadimIfsFgPj4eMTFxan/VqlU8PX1vc9Raps7t/5GZA5mzqy/EVmi1voeuVdLtf8Ysaf5zyEisiCiXTpxcHBAUFAQMjMzNcozMzMRGhqq8zkhISFa9ffv34/g4GD1uNjG6jRs05D9AoCjoyNcXFw0bkREJJ7W+h65F9t/IiI9CSLasWOHYG9vL6SmpgpnzpwRYmNjBWdnZ6GwsFAQBEFYuHChMGPGDHX9CxcuCG3atBEWLFggnDlzRkhNTRXs7e2Fzz//XF3n3//+t2Brayu8/fbbQn5+vvD2228LdnZ2wpEjR/Terz6USqUAQFAqlS3wShARmTdzbfNa43vkfsz1tSAiag3NafNETSwEQRDWrFkj+Pv7Cw4ODsLDDz8sHDp0SP3YrFmzhOHDh2vUP3jwoDBw4EDBwcFB6NKli5CSkqK1zc8++0zo2bOnYG9vL/Tq1UvYtWtXs/arD36xEJE1Mec2rzW+R5pizq8FEVFLa06bJ+rvWFgyrmNORNaEbd4f+FoQkTVpTpvH5SmIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhodmIHYKkafv5DpVKJHAkRUetraOv400ds/4nIujSn/WdiYaAbN24AAHx9fUWOhIjIdG7cuAFXV1exwxAV238iskb6tP/85W0D1dXV4erVq2jXrh1kMlmznqtSqeDr64tLly5Z5K+2Mn5xMX5xWWv8giDgxo0b8PHxgY2NdY+iNbT9t9bPjrlg/OKy9PgByz8GU7T/7LEwkI2NDTp37mzUNlxcXCzyg9mA8YuL8YvLGuO39p6KBsa2/9b42TEnjF9clh4/YPnH0Jrtv3VfdiIiIiIiohbBxIKIiIiIiIzGxEIEjo6OWLJkCRwdHcUOxSCMX1yMX1yMnwxl6a894xcX4xefpR+DKeLn5G0iIiIiIjIaeyyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCxM6K233kJoaCjatGmD9u3b66xTVFSEcePGwdnZGe7u7pg/fz6qqqpMG2gzdOnSBTKZTOO2cOFCscNq1Nq1axEQEAC5XI6goCBkZWWJHZJeEhMTtV5nLy8vscNq0uHDhzFu3Dj4+PhAJpPhyy+/1HhcEAQkJibCx8cHTk5OGDFiBE6fPi1OsDrcL/7Zs2drvSdDhgwRJ9h7JCUl4ZFHHkG7du3QqVMnTJgwAWfPntWoY+6vv9Sw/Rcf23/TYNsvLrHbfyYWJlRVVYWnn34af//733U+Xltbi7Fjx+LWrVv44YcfsGPHDuzatQsvvfSSiSNtnmXLlqG4uFh9e+2118QOSaf09HTExsYiISEBeXl5CAsLQ0REBIqKisQOTS99+/bVeJ1PnToldkhNunXrFgYMGIAPP/xQ5+PvvPMOVq5ciQ8//BDHjh2Dl5cXHn/8cdy4ccPEkep2v/gB4IknntB4TzIyMkwYYeMOHTqEefPm4ciRI8jMzERNTQ3Cw8Nx69YtdR1zf/2lhu2/uNj+mw7bfnGJ3v4LZHKbN28WXF1dtcozMjIEGxsb4cqVK+qytLQ0wdHRUVAqlSaMUH/+/v7C//3f/4kdhl4GDRokREdHa5T16tVLWLhwoUgR6W/JkiXCgAEDxA7DYACEL774Qv13XV2d4OXlJbz99tvqsjt37giurq7CunXrRIiwaffGLwiCMGvWLOGpp54SJZ7mKikpEQAIhw4dEgTB8l5/KWH7Lw62/+Jg2y8+U7f/7LEwIzk5OQgMDISPj4+6bPTo0aisrERubq6IkTVtxYoVcHNzw0MPPYS33nrLLLvuq6qqkJubi/DwcI3y8PBwZGdnixRV85w/fx4+Pj4ICAjA1KlTceHCBbFDMlhBQQEUCoXG++Ho6Ijhw4dbzPsBAAcPHkSnTp3Qo0cPzJ07FyUlJWKHpJNSqQQAdOzYEYB0Xn8pYfvfetj+mw+ptD2W0vYDpm//7YzeArUYhUIBT09PjbIOHTrAwcEBCoVCpKia9uKLL+Lhhx9Ghw4d8OOPPyI+Ph4FBQXYuHGj2KFpKC0tRW1trdbr6+npabav7d0GDx6Mbdu2oUePHvjtt9/w5ptvIjQ0FKdPn4abm5vY4TVbw2uu6/24ePGiGCE1W0REBJ5++mn4+/ujoKAAixcvxqOPPorc3Fyz+vEkQRAQFxeHP/3pTwgMDAQgjddfatj+tx62/+ZDCm2PpbT9gDjtP3ssjKRrUtW9t+PHj+u9PZlMplUmCILO8tbSnGNasGABhg8fjv79+yMqKgrr1q1DamoqysrKTBZvc9z7Opr6tTVUREQEJk2ahH79+mHUqFHYs2cPAGDr1q0iR2YcS30/ACAyMhJjx45FYGAgxo0bh2+//Rbnzp1Tvzfm4vnnn8d//vMfpKWlaT1mya+/OWD7z/bfFKTY/lvqewFYTtsPiNP+s8fCSM8//zymTp3aZJ0uXbrotS0vLy8cPXpUo+z3339HdXW1VmbZmow5poaVEX755RezupLi7u4OW1tbratTJSUlJn1tW4qzszP69euH8+fPix2KQRpWNFEoFPD29laXW+r7AQDe3t7w9/c3q/fkhRdewNdff43Dhw+jc+fO6nIpvv5iYPuvie2/aVhy+y/Ftscc235AvPafiYWR3N3d4e7u3iLbCgkJwVtvvYXi4mL1m71//344OjoiKCioRfahD2OOKS8vDwA0PqzmwMHBAUFBQcjMzMSf//xndXlmZiaeeuopESMzTGVlJfLz8xEWFiZ2KAYJCAiAl5cXMjMzMXDgQAD146APHTqEFStWiBydYcrKynDp0iWz+OwLgoAXXngBX3zxBQ4ePIiAgACNx6X4+ouB7b8mtv+mYcntvxTbHnNq+wEzaP+Nnv5Nert48aKQl5cnLF26VGjbtq2Ql5cn5OXlCTdu3BAEQRBqamqEwMBA4bHHHhN++ukn4bvvvhM6d+4sPP/88yJHrlt2drawcuVKIS8vT7hw4YKQnp4u+Pj4COPHjxc7NJ127Ngh2NvbC6mpqcKZM2eE2NhYwdnZWSgsLBQ7tPt66aWXhIMHDwoXLlwQjhw5Ijz55JNCu3btzDr2GzduqD/jANSflYsXLwqCIAhvv/224OrqKuzevVs4deqUMG3aNMHb21tQqVQiR16vqfhv3LghvPTSS0J2drZQUFAgHDhwQAgJCREeeOABs4j/73//u+Dq6iocPHhQKC4uVt8qKirUdcz99Zcatv/iYvtvOmz7xSV2+8/EwoRmzZolANC6HThwQF3n4sWLwtixYwUnJyehY8eOwvPPPy/cuXNHvKCbkJubKwwePFhwdXUV5HK50LNnT2HJkiXCrVu3xA6tUWvWrBH8/f0FBwcH4eGHH1Yvv2buIiMjBW9vb8He3l7w8fERJk6cKJw+fVrssJp04MABnZ/3WbNmCYJQv+TdkiVLBC8vL8HR0VEYNmyYcOrUKXGDvktT8VdUVAjh4eGCh4eHYG9vL/j5+QmzZs0SioqKxA5bEARBZ9wAhM2bN6vrmPvrLzVs/8XH9t802PaLS+z2X/a/IIiIiIiIiAzGVaGIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyILMC1a9fg5eWF5cuXq8uOHj0KBwcH7N+/X8TIiIioNbH9J0siEwRBEDsIIrq/jIwMTJgwAdnZ2ejVqxcGDhyIsWPHIjk5WezQiIioFbH9J0vBxILIgsybNw/fffcdHnnkEZw8eRLHjh2DXC4XOywiImplbP/JEjCxILIgt2/fRmBgIC5duoTjx4+jf//+YodEREQmwPafLAHnWBBZkAsXLuDq1auoq6vDxYsXxQ6HiIhMhO0/WQL2WBBZiKqqKgwaNAgPPfQQevXqhZUrV+LUqVPw9PQUOzQiImpFbP/JUjCxILIQr7zyCj7//HOcPHkSbdu2xciRI9GuXTv885//FDs0IiJqRWz/yVJwKBSRBTh48CCSk5Px8ccfw8XFBTY2Nvj444/xww8/ICUlRezwiIiolbD9J0vCHgsiIiIiIjIaeyyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMhoTCyIiIiIiMho/w/CdWWaxziyBAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets try to plot this for a bunch of x values1\n",
    "\n",
    "\n",
    "a = 2  # value of the first parameter\n",
    "b = 7  # value of the second parameter\n",
    "\n",
    "\n",
    "x_values = np.linspace(-10, 20, 1000)  # 1000 points\n",
    "pdf_values = [f(x,a,b) for x in x_values]\n",
    "cdf_values = [F(x,a,b) for x in x_values]   \n",
    "\n",
    "# Plotting the PDF and CDF\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x_values, pdf_values, label='PDF', color='blue')\n",
    "plt.title('Uniform Distribution PDF')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(x_values, cdf_values, label='CDF', color='orange')\n",
    "plt.title('Uniform Distribution CDF')\n",
    "plt.xlabel('x')    \n",
    "plt.ylabel('F(x)')\n",
    "plt.legend()\n",
    "plt.tight_layout()       \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbbf25ba",
   "metadata": {},
   "source": [
    "## Exponential Distribution\n",
    "\n",
    "PDf of an exponential Distribution can be given as :\n",
    "$$f(x)= \\lambda e^{-\\lambda x} \\quad \\text{for \\quad $0 \\le x$}$$\n",
    "and corresponding CDF can be given as :\n",
    "$$  F(x)= \\int_0 ^x f(x) dx =  1 - e^{-\\lambda x} \\quad  \\text{for \\quad $0 \\le x$} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4ef99e1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Exponential Distribution\n",
    "\n",
    "# Defining the probability density function (PDF) for the exponential distribution\n",
    "def f_exp(x,lam):\n",
    "    if x <0:\n",
    "        return 0\n",
    "    else:\n",
    "        return lam*np.exp(-lam*x)\n",
    "    \n",
    "#Defining the cumulative distribution function (CDF) for the exponential distribution\n",
    "def F_exp(x,lam):\n",
    "    if x < 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1 - np.exp(-lam*x)       \n",
    "    \n",
    "\n",
    "x_values = np.linspace(0, 20, 1000)  # 1000 points\n",
    "lam=0.3\n",
    "pdf_values = [f_exp(x,lam) for x in x_values]\n",
    "cdf_values = [F_exp(x,lam) for x in x_values]   \n",
    "# plotting\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x_values, pdf_values, label='PDF', color='blue')           \n",
    "plt.title('Exponential Distribution PDF')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.legend()     \n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(x_values, cdf_values, label='CDF', color='orange')\n",
    "plt.title('Exponential Distribution CDF')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('F(x)')\n",
    "plt.legend()\n",
    "plt.tight_layout()      \n",
    "\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d2f8fe00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7c11902bfed0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plottiing for the different values of lambda\n",
    "\n",
    "lambda_values = [0.2, 0.3, 0.5, 1.0]  # Different lambda values\n",
    "x_values = np.linspace(0, 20, 1000)  # 1000 points\\\n",
    "plt.figure(figsize=(8, 4))\n",
    "for lam in lambda_values:\n",
    "    plt.subplot(1, 2, 1)\n",
    "    pdf_values = [f_exp(x, lam) for x in x_values]\n",
    "    plt.plot(x_values, pdf_values, label=f'λ={lam}')  \n",
    "    plt.ylabel('f(x)') \n",
    "    plt.subplot(1, 2, 2)\n",
    "    cdf_values = [F_exp(x, lam) for x in x_values]\n",
    "    plt.plot(x_values, cdf_values, label=f'λ={lam}')\n",
    "    plt.ylabel('F(x)')\n",
    "\n",
    "\n",
    "\n",
    "plt.title('Exponential Distribution PDF for Different λ Values')\n",
    "\n",
    "plt.xlabel('x')\n",
    "\n",
    "plt.legend()    \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "316f1f41",
   "metadata": {},
   "source": [
    "## Gaussian  Distribution\n",
    "\n",
    "This is one of the import and ubiquitously seen distribution, and its better to understand the properties of this distribution.\n",
    "1. Parameters: $\\mu , \\sigma$\n",
    "2. Range : $(-\\infty,\\infty) $\n",
    "3. Notation we use Normal($\\mu , \\sigma$) pr N($\\mu , \\sigma$)\n",
    "The PDF of this function is given as :\n",
    "$$  f(x) = \\frac{1}{\\sigma\\sqrt{2 \\pi}} e^{-\\left( x- \\mu\\right)^2 /2 \\sigma^2} $$\n",
    "CDFs is give as :\n",
    "$$F(x)=\\int_{-\\infty} ^{x} f(x) dx    \\$$\n",
    "\n",
    "\n",
    "\n",
    "Using the definition of the error function:\n",
    "\\begin{equation*}\n",
    "\\operatorname{erf}(x) = \\frac{2}{\\sqrt{\\pi}} \\int_0^x e^{-u^2} \\, du\n",
    "\\end{equation*}\n",
    "\n",
    "we obtain:\n",
    "\\begin{equation*}\n",
    "F(x) = \\frac{1}{2} \\left[1 + \\operatorname{erf}\\left(\\frac{x - \\mu}{\\sqrt{2}\\sigma}\\right)\\right]\n",
    "\\end{equation*}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf1564fa",
   "metadata": {},
   "source": [
    "## Exercise \n",
    "####  1. Problem : Derive this form of the CFD of a Normal distribution in terms of an error functions.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c794b958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.special import erf\n",
    "from scipy.stats import norm\n",
    "# ----------------------------------------\n",
    "# Gaussian PDF\n",
    "# ----------------------------------------\n",
    "def f_normal(x, mu, sigma):\n",
    "\n",
    "    return (\n",
    "        1/(sigma*np.sqrt(2*np.pi))\n",
    "    ) * np.exp(\n",
    "        -0.5*((x-mu)/sigma)**2\n",
    "    )\n",
    "\n",
    "# ----------------------------------------\n",
    "# Numerical integration CDF using quad\n",
    "# ----------------------------------------\n",
    "def F_normal_quad(x, mu, sigma):\n",
    "\n",
    "    result, error = quad(\n",
    "        f_normal,\n",
    "        -1e1000,\n",
    "        x,\n",
    "        args=(mu, sigma)\n",
    "    )\n",
    "\n",
    "    return result\n",
    "\n",
    "# ----------------------------------------\n",
    "# Exact analytical CDF\n",
    "# ----------------------------------------\n",
    "def F_normal_exact(x, mu, sigma):\n",
    "\n",
    "    return 0.5 * (\n",
    "        1 + erf((x-mu)/(sigma*np.sqrt(2)))\n",
    "    )\n",
    "\n",
    "\n",
    "# ----------------------------------------\n",
    "# Using scipy.stats.norm for exact CDF\n",
    "# ----------------------------------------\n",
    "def F_normal_scipy(x, mu, sigma):\n",
    "\n",
    "    return norm.cdf(x, loc=mu, scale=sigma)\n",
    "    \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# ----------------------------------------\n",
    "# Parameters\n",
    "# ----------------------------------------\n",
    "mu = 0\n",
    "sigma = 1\n",
    "\n",
    "x_values = np.linspace(-5,5,200)\n",
    "\n",
    "# ----------------------------------------\n",
    "# Compute numerical CDF\n",
    "# ----------------------------------------\n",
    "cdf_quad = [\n",
    "    F_normal_quad(x, mu, sigma)\n",
    "    for x in x_values\n",
    "]\n",
    "\n",
    "# ----------------------------------------\n",
    "# Exact CDF\n",
    "# ----------------------------------------\n",
    "cdf_exact = [\n",
    "    F_normal_exact(x, mu, sigma)\n",
    "    for x in x_values\n",
    "]\n",
    "\n",
    "\n",
    "# ----------------------------------------\n",
    "#  CDF using scipy.stats.norm\n",
    "# ----------------------------------------\n",
    "cdf_scipy= [\n",
    "    F_normal_scipy(x, mu, sigma)\n",
    "    for x in x_values\n",
    "]\n",
    "\n",
    "\n",
    "\n",
    "# ----------------------------------------\n",
    "# Plot\n",
    "# ----------------------------------------\n",
    "plt.figure(figsize=(7,5))\n",
    "\n",
    "plt.plot(\n",
    "    x_values,\n",
    "    cdf_quad,\n",
    "    label='Numerical CDF (quad)'\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    x_values,\n",
    "    cdf_exact,\n",
    "    '--',\n",
    "    label='Exact CDF'\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(\n",
    "    x_values,\n",
    "    cdf_scipy,\n",
    "    ':',\n",
    "    label='CDF using scipy.stats.norm'\n",
    ")\n",
    "\n",
    "\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"F(x)\")\n",
    "\n",
    "plt.title(\"Gaussian CDF using quad\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c332c132",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting for different values of mu and sigma\n",
    "mu_values = [0, 3, 10]  # Different mean values\n",
    "sigma_values = [1, 2, 3]  # Different standard deviation values\n",
    "x_values = np.linspace(-10, 20, 1000)  # 1000 points\n",
    "plt.figure(figsize=(12, 6))\n",
    "for mu,sigma in zip(mu_values, sigma_values):        \n",
    "    plt.subplot(1, 2, 1)\n",
    "    pdf_values = [f_normal(x, mu, sigma) for x in x_values]\n",
    "    plt.plot(x_values, pdf_values, label=f'μ={mu}, σ={sigma}')  \n",
    "    plt.ylabel('f(x)') \n",
    "    plt.subplot(1, 2, 2)\n",
    "    cdf_values = [F_normal_exact(x, mu, sigma) for x in x_values]\n",
    "    plt.plot(x_values, cdf_values, label=f'μ={mu}, σ={sigma}')\n",
    "    plt.ylabel('F(x)')\n",
    "plt.xlabel('x')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d8c6a9b",
   "metadata": {},
   "source": [
    "## Normal distribution \n",
    "Now the normal distribution is when we take the $\\mu=0$ and the $\\sigma=1$ for the Gaussian and is denoted by:\n",
    "$$N(z:0,1)=   \\frac{1}{\\sqrt{2 \\pi}} e^{-z^2/2}   $$\n",
    "\n",
    "### Normal Probabilities\n",
    "Rule of thumb: The values of the probabilites for the range of z in the intervals as given below are:\n",
    "1.  $P(-1\\le z \\le 1) \\approx 0.68$\n",
    "2.  $P(-2\\le z \\le 2) \\approx 0.95$\n",
    "3.  $P(-3\\le z \\le 3) \\approx 0.99$\n",
    "\n",
    "\n",
    "The CDF of this is given as \n",
    "$$\\Phi(z)= \\int_{-\\infty}^z N(x) dx$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11bc641f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Defining a Normal Distributionand computing its 1sigma, 2 sigma, 3 sigma area:\n",
    "\n",
    "\n",
    "def Normal(z):\n",
    "    return (1 / np.sqrt(2 * np.pi)) * np.exp(-0.5 * z**2)\n",
    "\n",
    "z= np.linspace(-5, 5, 1000)\n",
    "pdf_values = [Normal(z_i) for z_i in z]\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(z, pdf_values, label='Standard Normal Distribution')\n",
    "plt.fill_between(z, pdf_values, where=(z >= -1) & (z <= 1), color='red', alpha=0.5, label='1σ Area')\n",
    "plt.fill_between(z, pdf_values, where=(z >= -2) & (z <= 2), color='orange', alpha=0.4, label='2σ Area')\n",
    "plt.fill_between(z, pdf_values, where=(z >= -3) & (z <= 3), color='blue', alpha=0.3, label='3σ Area')\n",
    "plt.title('Standard Normal Distribution with σ Areas')\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('f(z)')\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65da93d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Cumulative distribution of the standard normal distribution\n",
    "z= np.linspace(-5, 5, 1000)\n",
    "cdf_values = [F_normal_exact(z_i, 0, 1) for z_i in z]\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(z, cdf_values, label='CDF of Standard Normal Distribution', color='green')      \n",
    "plt.title('CDF of Standard Normal Distribution')\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('F(z)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5fc9cd",
   "metadata": {},
   "source": [
    "## Exercise \n",
    "You can notice that this function is symmetric about z=0 \n",
    "\n",
    " 1.Based on the  rule fo thumb $P(-1\\le z \\le 1) \\approx 0.68$ and the symmetry properties of the Normal distribution ,estimate $\\Phi(1)$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ccfa17e",
   "metadata": {},
   "source": [
    "## Pareto Distributions\n",
    "\n",
    " You have so far seen multiple distributions and their paramters. Now try to define a function in python for a distribution given as :$$f(x)= \\frac{\\alpha m^\\alpha}{x^{\\alpha+1} }$$\n",
    "\n",
    " which is called a Pareto Distributions with  the properties are:\n",
    "1. Parameters : m>0 , $\\alpha >0$\n",
    " 2. Range : [m , $ \\infty$]\n",
    "\n",
    "Plot if for the different pairs of m and $\\alpha$ : (m,$\\alpha$)=[(1,2), (3,6), (2,6)]\n",
    " and find out the CDF for this distribution and plot it for the pairs of m and $\\alpha$ as given above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "38d91848",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# ---------------------------------------------------\n",
    "# Pareto PDF\n",
    "# ---------------------------------------------------\n",
    "def pareto_pdf(x, m, alpha):\n",
    "    \"\"\"\n",
    "    Pareto probability density function\n",
    "    \"\"\"\n",
    "    pdf = np.zeros_like(x)\n",
    "\n",
    "    # valid region x >= m\n",
    "    mask = x >= m\n",
    "\n",
    "    pdf[mask] = (alpha * m**alpha) / (x[mask]**(alpha + 1))\n",
    "\n",
    "    return pdf\n",
    "\n",
    "\n",
    "# ---------------------------------------------------\n",
    "# Pareto CDF\n",
    "# ---------------------------------------------------\n",
    "def pareto_cdf(x, m, alpha):\n",
    "    \"\"\"\n",
    "    Pareto cumulative distribution function\n",
    "    \"\"\"\n",
    "    cdf = np.zeros_like(x)\n",
    "\n",
    "    # valid region x >= m\n",
    "    mask = x >= m\n",
    "\n",
    "    cdf[mask] = 1 - (m / x[mask])**alpha\n",
    "\n",
    "    return cdf\n",
    "\n",
    "\n",
    "# ---------------------------------------------------\n",
    "# Parameter sets\n",
    "# ---------------------------------------------------\n",
    "params = [\n",
    "    (1, 2),\n",
    "    (3, 6),\n",
    "    (2, 6)\n",
    "]\n",
    "\n",
    "# x range\n",
    "x = np.linspace(-2, 10, 1000)\n",
    "\n",
    "# ---------------------------------------------------\n",
    "# Plot PDFs\n",
    "# ---------------------------------------------------\n",
    "plt.figure(figsize=(8, 5))\n",
    "\n",
    "for m, alpha in params:\n",
    "    y = pareto_pdf(x, m, alpha)\n",
    "    plt.plot(x, y, label=fr\"$m={m}, \\alpha={alpha}$\")\n",
    "\n",
    "plt.title(\"Pareto Distribution PDF\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# ---------------------------------------------------\n",
    "# Plot CDFs\n",
    "# ---------------------------------------------------\n",
    "plt.figure(figsize=(8, 5))\n",
    "\n",
    "for m, alpha in params:\n",
    "    y = pareto_cdf(x, m, alpha)\n",
    "    plt.plot(x, y, label=fr\"$m={m}, \\alpha={alpha}$\")\n",
    "\n",
    "plt.title(\"Pareto Distribution CDF\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"F(x)\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d55badb4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "bf7f0be9",
   "metadata": {},
   "source": [
    "# Joint Probability Distribution Function\n",
    "\n",
    "Suppose we have two random variables, \\(X\\) and \\(Y\\), described by a joint probability density function \\(f(x,y)\\).\n",
    "\n",
    "The probability that:\n",
    "\n",
    "- \\(X\\) lies between \\(x\\) and \\(x+dx\\), and  \n",
    "- \\(Y\\) lies between \\(y\\) and \\(y+dy\\)\n",
    "\n",
    "is given by\n",
    "\n",
    "$$\n",
    "f(x,y)\\,dx\\,dy .\n",
    "$$\n",
    "\n",
    "Here, \\(f(x,y)\\) is called the **joint probability density function (joint PDF)** of the random variables \\(X\\) and \\(Y\\).\n",
    "\n",
    "It describes how probability is distributed simultaneously over the two variables. The quantity\n",
    "\n",
    "$$\n",
    "f(x,y)\\,dx\\,dy\n",
    "$$\n",
    "\n",
    "represents the probability contained in a small area element \\(dx\\,dy\\) around the point \\((x,y)\\)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b71b702c",
   "metadata": {},
   "source": [
    "## Example: Cosmic Ray Detection\n",
    "\n",
    "A cosmic ray detector measures two quantities for every detected event:\n",
    "\n",
    "* $E$: the energy of the particle (in TeV),\n",
    "* $\\theta$: the zenith angle of arrival (in degrees).\n",
    "\n",
    "Suppose the detector records events according to a joint probability density function\n",
    "\n",
    "$$\n",
    "f(E,\\theta).\n",
    "$$\n",
    "\n",
    "NOw assuming these two $E$ and $\\theta$ follows :\n",
    "\n",
    "* E from an exponential distribution with scale 2 TeV,\n",
    "* $\\theta$ from a normal distribution centered around  $\\pi/4$, with standard deviation 1.\n",
    " and are indenpendent of each another (this is not the case in reality)\n",
    "Using this informatin.\n",
    "\n",
    "1.  Plot the joint distribution of E and $\\theta$ using a scatter plot.\n",
    "\n",
    "\n",
    "\n",
    "2. Estimate the joint probability both numerically and analytically \n",
    "\n",
    "$$\n",
    "P(2<E<5,\\pi/6\\le\\theta\\le \\pi/3).\n",
    "$$\n",
    "\n",
    "3. Obtain the marginal distribution of energy and plot it.\n",
    "\n",
    "$$\n",
    "f_E(E),\n",
    "$$\n",
    "\n",
    "by ignoring the angular information.\n",
    "\n",
    "4. Obtain the marginal distribution of zenith angle adn plot it.\n",
    "\n",
    "$$\n",
    "f_\\theta(\\theta),\n",
    "$$\n",
    "\n",
    "by ignoring the energy information.\n",
    "\n",
    "5. Explain physically what information is contained in:\n",
    "\n",
    "* the joint probability distribution,\n",
    "* the marginal probability distributions.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "739c0c77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x75ef09d4e490>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Example of joint probability distribution function (PDF) for two independent normal distributions\n",
    "\n",
    "np.random.seed(0)  # For reproducibility\n",
    "\n",
    "E= np.random.exponential(scale=2, size=1000)  # 1000 samples from an exponential distribution\n",
    "\n",
    "theta= np.random.normal(np.pi/4,1, size=1000)  # 1000 samples from a normal distribution\n",
    "\n",
    "\n",
    "\n",
    "plt.scatter(E, theta, alpha=0.5)\n",
    "plt.title('Joint PDF of f(E, theta)')\n",
    "plt.xlabel(r'$E$ (TeV)')\n",
    "plt.ylabel(r'$\\theta$ (radians)')   \n",
    "plt.axvline(2, color='red', linestyle='--', label=r'$E=2$')  # Adding a horizontal line at y=2\n",
    "plt.axvline(5, color='red', linestyle='--', label=r'$E=5$')  # Adding a horizontal line at y=4\n",
    "plt.axhline(np.pi/6, color='black', linestyle='--', label=r'$\\theta=\\pi/6$')  # Adding a vertical line at x=1 \n",
    "plt.axhline(np.pi/3, color='black', linestyle='--', label=r'$\\theta=\\pi/3$')  # Adding a vertical line at x=3\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4422ca1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated Probability Numerical = 0.0565\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "# Generate random samples\n",
    "E= np.random.exponential(scale=2, size=10000)  # 10000 samples from an exponential distribution\n",
    "\n",
    "theta= np.random.normal(np.pi/4,1, size=10000)  # 10000 samples from a normal distribution\n",
    "\n",
    "\n",
    "# Monte Carlo estimate of probability\n",
    "P = np.mean((E > 2) & (E < 5) & (theta > np.pi/6) & (theta < np.pi/3))\n",
    "\n",
    "print(\"Estimated Probability Numerical =\", P)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd464f77",
   "metadata": {},
   "source": [
    "### Analytical Solution for the Joint Probability\n",
    "\n",
    "Since $X$ and $Y$ are independent, their joint probability density function (PDF) is the product of their individual PDFs:\n",
    "$$\n",
    "f(x,y) = f_X(x)f_Y(y)\n",
    "$$\n",
    "\n",
    "Therefore, the joint probability over the specified intervals factors into two independent single integrals:\n",
    "$$\n",
    "P(2 < X < 5, \\; \\pi/6 < Y < \\pi/3) = P(2 < X < 5) \\cdot P(\\pi/6 < Y < \\pi/3)\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### Part 1: Exponential Distribution ($X$)\n",
    "The energy $X$ follows an exponential distribution with a scale parameter of $2\\text{ TeV}$:\n",
    "$$\n",
    "X \\sim \\text{Exponential}(\\text{scale} = 2) \\implies \\lambda = \\frac{1}{2}\n",
    "$$\n",
    "\n",
    "The probability density function is:\n",
    "$$\n",
    "f_X(x) = \\frac{1}{2} e^{-x/2}, \\qquad x > 0\n",
    "$$\n",
    "\n",
    "Evaluating the probability for the interval $2 < X < 5$:\n",
    "$$\n",
    "P(2 < X < 5) = \\int_2^5 \\frac{1}{2} e^{-x/2} \\, dx\n",
    "$$\n",
    "$$\n",
    "= \\left[ -e^{-x/2} \\right]_2^5\n",
    "$$\n",
    "$$\n",
    "= \\left( -e^{-5/2} \\right) - \\left( -e^{-2/2} \\right)\n",
    "$$\n",
    "$$\n",
    "= e^{-1} - e^{-5/2}\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### Part 2: Normal Distribution ($Y$)\n",
    "The angle $Y$ follows a normal distribution with mean $\\mu = \\pi/4$ and variance $\\sigma^2 = 1$:\n",
    "$$\n",
    "Y \\sim \\mathcal{N}(\\pi/4, 1)\n",
    "$$\n",
    "\n",
    "The probability density function is:\n",
    "$$\n",
    "f_Y(y) = \\frac{1}{\\sqrt{2\\pi}} \\exp\\left[ -\\frac{(y - \\pi/4)^2}{2} \\right]\n",
    "$$\n",
    "\n",
    "Evaluating the probability for the interval $\\pi/6 < Y < \\pi/3$:\n",
    "$$\n",
    "P(\\pi/6 < Y < \\pi/3) = \\int_{\\pi/6}^{\\pi/3} \\frac{1}{\\sqrt{2\\pi}} \\exp\\left[ -\\frac{(y - \\pi/4)^2}{2} \\right] dy\n",
    "$$\n",
    "\n",
    "Standardize the variable using $Z = \\frac{Y - \\mu}{\\sigma} = Y - \\pi/4$:\n",
    "- When $y = \\pi/6$: \n",
    "  $$z = \\frac{\\pi}{6} - \\frac{\\pi}{4} = -\\frac{\\pi}{12}$$\n",
    "- When $y = \\pi/3$: \n",
    "  $$z = \\frac{\\pi}{3} - \\frac{\\pi}{4} = \\frac{\\pi}{12}$$\n",
    "\n",
    "Using the standard normal cumulative distribution function $\\Phi(z)$:\n",
    "$$\n",
    "P(\\pi/6 < Y < \\pi/3) = \\Phi\\left(\\frac{\\pi}{12}\\right) - \\Phi\\left(-\\frac{\\pi}{12}\\right)\n",
    "$$\n",
    "\n",
    "Using the symmetry property $\\Phi(-z) = 1 - \\Phi(z)$:\n",
    "$$\n",
    "P(\\pi/6 < Y < \\pi/3) = \\Phi\\left(\\frac{\\pi}{12}\\right) - \\left[1 - \\Phi\\left(\\frac{\\pi}{12}\\right)\\right]\n",
    "$$\n",
    "$$\n",
    "= 2\\Phi\\left(\\frac{\\pi}{12}\\right) - 1\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "### Final Combined Result\n",
    "Multiplying both independent probabilities together gives the final exact analytical expression:\n",
    "$$\n",
    "P(2 < X < 5, \\; \\pi/6 < Y < \\pi/3) = \\left( e^{-1} - e^{-5/2} \\right) \\cdot \\left[ 2\\Phi\\left(\\frac{\\pi}{12}\\right) - 1 \\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1aaef29e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard Norma (0.5) = 0.6033\n",
      " Estimated Probability Analytically  = 0.0590\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "phi_05 = norm.cdf(np.pi/12, loc=0, scale=1)\n",
    "\n",
    "print(f\"Standard Norma (0.5) = {phi_05:.4f}\") \n",
    "\n",
    "P=( np.exp(-1)- np.exp(-5/2)) * (  2* phi_05 - 1)\n",
    "print(f\" Estimated Probability Analytically  = {P:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b4ccf75",
   "metadata": {},
   "source": [
    "\n",
    "Hence the final ans we see  is ,\n",
    "$$\n",
    "P(2 < X < 5, \\; \\pi/6 < Y < \\pi/3) = \\left( e^{-1} - e^{-5/2} \\right) \\cdot \\left[ 2\\Phi\\left(\\frac{\\pi}{12}\\right) - 1 \\right] \\\\\n",
    "\n",
    "\n",
    "          =0.0590\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb18b2b1",
   "metadata": {},
   "source": [
    "Now lets plot the marginal distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4939e928",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# -----------------------------------\n",
    "# Marginal Distribution of E\n",
    "# -----------------------------------\n",
    "\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "\n",
    "plt.hist(E, bins=40, density=True, alpha=0.7)\n",
    "\n",
    "plt.xlabel(r'$E$ (TeV)')\n",
    "plt.ylabel('Probability Density')\n",
    "\n",
    "plt.title(r'Marginal Distribution $f_E(E)$')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Functional form of the marginal distribution of E    \n",
    "def f_E(E, lam):\n",
    "    if E < 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return lam * np.exp(-lam * E)   \n",
    "E_values = np.linspace(0, 20, 1000)\n",
    "lam = 1/2\n",
    "pdf_values = [f_E(E, lam) for E in E_values]\n",
    " \n",
    "plt.plot(E_values, pdf_values, label=f'λ={lam}', color='blue')\n",
    "plt.title('Marginal Distribution $f_E(E)$')\n",
    "plt.xlabel(r'$E$ (TeV)')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# -----------------------------------\n",
    "# Marginal Distribution of theta\n",
    "# -----------------------------------\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "\n",
    "plt.hist(theta, bins=40, density=True, alpha=0.7)\n",
    "\n",
    "# Tick marks in multiples of pi\n",
    "plt.xticks(\n",
    "    [0, np.pi/6, np.pi/4, np.pi/3, np.pi/2, np.pi],\n",
    "    [r'$0$',\n",
    "     r'$\\pi/6$',\n",
    "     r'$\\pi/4$',\n",
    "     r'$\\pi/3$',\n",
    "     r'$\\pi/2$',\n",
    "     r'$\\pi$']\n",
    ")\n",
    "\n",
    "\n",
    "plt.xlabel(r'$\\theta$ (radians)')\n",
    "plt.ylabel('Probability Density')\n",
    "\n",
    "plt.title(r'Marginal Distribution $f_\\theta(\\theta)$')\n",
    "\n",
    "\n",
    "# Functional form of the marginal distribution of theta\n",
    "def f_theta(theta, mu, sigma):\n",
    "    return (1 / (sigma * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((theta - mu) / sigma) ** 2)\n",
    "\n",
    "theta_values = np.linspace(-2, 4, 1000)\n",
    "mu = np.pi/4\n",
    "sigma = 1\n",
    "pdf_values = [f_theta(theta, mu, sigma) for theta in theta_values]  \n",
    "plt.plot(theta_values, pdf_values, label=f'μ={mu}, σ={sigma}', color='orange')\n",
    "plt.title('Marginal Distribution $f_\\\\theta(\\\\theta)$')\n",
    "plt.xlabel(r'$\\theta$ (radians)')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a2c0cb7",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Here  in the above 2d scatter plot:\n",
    "\n",
    "- \\(X\\) is drawn from an exponential distribution.\n",
    "- \\(Y\\) is drawn from a normal distribution.\n",
    "- Since \\(X\\) and \\(Y\\) are independent, the joint PDF is\n",
    "\n",
    "$$\n",
    "f(x,y)=f_X(x)f_Y(y).\n",
    "$$\n",
    "\n",
    "The scatter plot shows random samples from this joint distribution.\n",
    "\n",
    "The rectangle bounded by\n",
    "\n",
    "$$\n",
    "1 < x < 3\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "4 < y < 6\n",
    "$$\n",
    "\n",
    "corresponds to the probability\n",
    "\n",
    "$$\n",
    "P(1<X<3,\\;4<Y<6).\n",
    "$$\n",
    "\n",
    "This probability can be estimated by counting the fraction of sampled points lying inside the rectangle."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e47ed343",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b03e29c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3a70a40b",
   "metadata": {},
   "source": [
    "# Transformation of Random Variables\n",
    "Say if X is a random variable and has $f_X(x)$ , $F_X(x)$ as the pdf and cdf what would be the corresponding pdf and cdf of Y which relates to X as \n",
    "$Y=Y(X)$ or in simple terms Y is a function of X.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbb0e0e9",
   "metadata": {},
   "source": [
    "#### Example 1 with Gaussian Distribution\n",
    "We have a Gaussian Distributino mith mean and varian given as $\\mu,\\sigma^2$ and the pdf is given as :\n",
    "$$\n",
    "f(x)= \\frac{1}{\\sqrt{2\\pi}\\,\\sigma} \\, e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f1a7e44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "mean = 4\n",
    "sigma = 2  \n",
    "\n",
    "X = np.random.normal(mean, sigma, 1000)\n",
    "\n",
    "# Histogram (normalized!)\n",
    "plt.hist(X, bins=30, density=True)\n",
    "\n",
    "# to plot the Gaussian Curve\n",
    "x_vals = np.linspace(min(X), max(X), 200)\n",
    "\n",
    "# Gaussian PDF\n",
    "pdf = (1/(sigma * np.sqrt(2*np.pi))) * np.exp(-(x_vals - mean)**2 / (2*sigma**2))\n",
    "\n",
    "# Plot smooth curve\n",
    "plt.plot(x_vals, pdf)\n",
    "\n",
    "plt.title('Normal Distribution with mean=4 and std=2')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Density')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5632bbe1",
   "metadata": {},
   "source": [
    "Now we change the variables of this function to z given as :\n",
    "$$z= \\frac{x-\\mu}{\\sigma}$$\n",
    "We will simply get a standard Normal Distribution. \n",
    "$$f_Z(z) = \\frac{1}{\\sqrt{2\\pi}} \\exp\\left( -\\frac{z^2}{2} \\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58b8389f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Standardization\n",
    "Z = (X - mean) / sigma\n",
    "\n",
    "# Histogram\n",
    "plt.hist(Z, bins=30, density=True,color='red',alpha=0.5)\n",
    "\n",
    "# Smooth z values\n",
    "z_vals = np.linspace(min(Z), max(Z), 200)\n",
    "\n",
    "# Standard normal PDF\n",
    "pdf = (1/np.sqrt(2*np.pi)) * np.exp(-z_vals**2 / 2)\n",
    "\n",
    "# Plot curve\n",
    "plt.plot(z_vals, pdf,color='red')\n",
    "\n",
    "plt.title('Standardized Normal Distribution')\n",
    "plt.xlabel('Z')\n",
    "plt.ylabel('Density')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0c3852b",
   "metadata": {},
   "source": [
    "#### Example 2 : Exponential Distribution with parameter $\\lambda$\n",
    "The pdf for this function is given as:\n",
    "$$f(x)=\\lambda e^{-\\lambda x}$$\n",
    "Now define a transformed variable:\n",
    "$$\n",
    "Y = X^2\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "###  Exercise \n",
    "\n",
    "1. **Find the PDF of $Y$ analytically** using the change of variables method.\n",
    "\n",
    "2. **Simulate $X$ numerically**, compute $Y = X^2$, and plot the histogram of $Y$.  \n",
    "   Overlay the analytical expression of $f_Y(y)$ on top of the histogram.\n",
    "\n",
    "3. **Derive the cumulative distribution functions (CDFs):**\n",
    "   - $F_X(x)$ for the original variable\n",
    "   - $F_Y(y)$ for the transformed variable\n",
    "\n",
    "4. **Plot both CDFs on the same figure** for comparison.\n",
    "\n",
    "\n",
    "###  Additional Task (Optional but Recommended)\n",
    "\n",
    "5. Verify numerically that:\n",
    "$$\n",
    "F_Y(y) = P(Y \\le y) = P(X \\le \\sqrt{y})\n",
    "$$\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gammapy_env",
   "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": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
