2-2. 확률 분포.ipynb

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     "text": [
      "pandas 0.25.1\n",
      "numpy 1.18.5\n",
      "scipy 1.5.2\n",
      "matplotlib 3.5.3\n",
      "seaborn 0.12.2\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "for i in [pd, np, scipy, mpl, sns]:\n",
    "    print(i.__name__, i.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8dca9fb",
   "metadata": {},
   "source": [
    "# 2-2 확률 분포\n",
    "\n",
    "\n",
    "#### 확률 변수\n",
    "\n",
    "- 확률적인 과정의 결과를 수치적으로 표현하기 위한 임의의 수입니다. (일반적으로 대문자로 표기)\n",
    "\n",
    "\n",
    "#### 기대값 E[X]\n",
    "\n",
    "- 확률 변수의 평균적인 예상값으로 중심 경향성을 표현합니다. \n",
    "\n",
    "> $E[X + Y] = E[X] + E[Y]$\n",
    ">\n",
    "> $E[aX] = aE[X]$\n",
    "\n",
    "#### 분산 V(X)\n",
    "\n",
    "- 데이터의 변동 정도를 측정하는 지표로 사용되며, 데이터가 중심(평균)으로 부터 흩어진 정도를 나타내는 지표입니다.\n",
    "\n",
    "> $V(X)= E[(X - E[X])^2]=E[X^2] - E[X]^2$\n",
    ">\n",
    "> $V(X + Y)= V(X) + 2COV(X,Y) + V(Y)$\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px; margin-left: 50px;\">\n",
    "\n",
    "$V(X + Y) = E[(X + Y - E[X + Y])^2] = E[(X - E(X) + Y - E(Y))^2]$\n",
    "\n",
    "$= E[X^2] - E(X)^2 + E[Y^2] - E(Y)^2 + 2E[(X - E[X])(Y - E[Y])] = V(X) + V(Y)+ 2COV(X,Y)$\n",
    "\n",
    "</div>\n",
    "\n",
    "> $V(aX)=a^2V(X)$\n",
    "\n",
    "> $V(-aX)=a^2V(X)$\n",
    "\n",
    "#### 공분산 COV(X, Y)\n",
    "\n",
    "- 두 변수가 함께 변하는 정도를 나타냅니다.\n",
    "\n",
    "> $COV(X, Y)=E[(X - E[X])(Y - E[Y])]=E[XY] - E[X][E[Y]$\n",
    "\n",
    "- 두 변수가 독립이라면, $COV(X,Y) = 0$이 됩니다.\n",
    "\n",
    "> **이 경우**, $V(X + Y) = V(X) + V(Y)$ 가 됩니다.\n",
    "\n",
    "#### 표본평균의 모평균과 모분산\n",
    "\n",
    "- 표본평균은 가설 검정과 신뢰구간등 두루 사용되는 통계량입니다.\n",
    "\n",
    "\n",
    "- 표본평균도 확률 변수입니다. 표본평균의 모평균과 모분산을 대상 확률 변수의 모평균과 모분산에서 유도해 봅니다.\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "모평균이 $\\mu$, 모분산이 $\\sigma^2$인 모집단에서 n개의 표본을 추출했습니다.\n",
    "    \n",
    "> $X_1, X_2, X_3, ... X_n$\n",
    "\n",
    "표본평균 $\\bar{X}$는\n",
    "\n",
    "> $\\bar{X}= \\frac{(X_1 + X_2 + ... + X_n)}{n} $\n",
    "\n",
    "입니다.\n",
    "\n",
    "> $E(\\bar{X})= E(\\frac{X_1 + X_2 + ... + X_n}{n}) = \\frac{E(X_1) + E(X_2) + .. E(X_n)}{n} $\n",
    "\n",
    "$X_1, ... X_n$의 모평균이 $\\mu$이므로 $E(X_1), ... E(X_n)$ 모두 $\\mu$ 입니다.\n",
    "\n",
    "> 따라서, $E(\\bar{X}) = \\frac{n\\mu}{n} = \\mu$\n",
    "\n",
    "$V(\\bar{X}) = V(\\frac{X_1 + X_2 + ... + X_n}{n})$ 입니다.\n",
    "    \n",
    "**n개의 표본이 서로 독립이라면,**\n",
    "\n",
    "$X_1, ... X_n$ 간의 공분산은 모두 $COV(X_1, X_2) = 0, ... COV(X_{n-1}, X_n) = 0$ 입니다.\n",
    "\n",
    "> $V(\\bar{X}) = V(\\frac{X_1}{n}) + V(\\frac{X_2}{n}) ... + V(\\frac{X_n}{n})$\n",
    "\n",
    "$X_1, ... X_n$은 모두 분산이 $\\sigma^2$이므로 $V(X_1), ... V(X_n)$ 모두 $\\sigma^2$ 이고, $V(aX) = a^2V(X)$이므로\n",
    "\n",
    "> $V(\\bar{X}) = \\frac{\\sigma^2}{n^2} + \\frac{\\sigma^2}{n^2}... + \\frac{\\sigma^2}{n^2} = \\frac{\\sigma^2}{n}$ 이 됩니다.\n",
    "\n",
    "</div>"
   ]
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   "id": "1fad986e",
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   "source": [
    "## 1. 이산형 확률 분포\n",
    "\n",
    "- 이산형(Discrete) 확률 변수가 취하는 값에 대한 확률을 나타내는 분포\n",
    "\n",
    "|분포|확률 변수|매개변수|확률 질량 함수|E(X)|V(X)|\n",
    "|----|:---------|:--------------|:----|---|---|\n",
    "|베르누이(Bernoulii) 분포|베르누이 시행(0 또는 1)의 결과|p: 1이 나올 확률|$p(1)=p$|$p$|$$p\\left(1-p\\right)$$|\n",
    "|이항(Binomial) 분포|연속된 n번의 베르누이 시행에서 n번 중 1이 나온 횟수|p: 1이 나올 확률, n: 총 시행수|$$p(x)={n \\choose x}p^x(1-p)^{n-x}$$|$np$|$np(1-p)$|\n",
    "|푸아송(Poisson) 분포|단위 시간 또는 공간에서 발생하는 사건수|$$\\lambda$$: 단위 시간 또는 공간에서 발생하는 평균 사건수|$$p(x)=\\frac{e^{-\\lambda}(\\lambda)^x}{x!}$$|$\\lambda$|$\\lambda$|\n"
   ]
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   "id": "6188c8fa",
   "metadata": {},
   "source": [
    "## 2. 연속형 확률 분포\n",
    "\n",
    "- 연속형(Continuous)  확률 변수가 취하는 값에 대한 확률을 나타내는 분포\n",
    "\n",
    "|분포|확률 변수|매개변수|확률 밀도 함수|E(X)|V(X)|\n",
    "|---|:---|:---|:-------|:---:|:---:|\n",
    "|지수(Exponential) 분포|다음 사건이 발생하는 시간|$\\lambda$:단위 또는 시간 공간에서 발생하는 평균 사건 수|$$\\lambda e^{-\\lambda x}$$|$$\\frac{1}{\\lambda}$$|$$\\frac{1}{\\lambda^2}$$|\n",
    "|감마(Gamma) 분포|다음 $\\alpha$개의 사건이 발생하는 평균 시간|$\\alpha$: 사건의 발생 횟수, $\\beta$: 단위 시간 또는 공간에서 발생하는 평균 사건수|$$\\frac{\\beta^\\alpha x^{\\alpha-1} e^{-\\beta x}}{\\Gamma(\\alpha)}$$|$$\\frac{\\alpha}{\\beta}$$|$$\\frac{\\alpha}{\\beta^2}$$|\n",
    "|정규(Normal) 분포|좌우 대칭의 종모양 분포|$\\mu$:평균, $\\sigma^2$: 분산|$$\\frac{1}{\\sigma\\sqrt{2 \\pi}}e^{-\\frac{(x-\\mu)^2}{2 \\sigma^2}}$$|$$\\mu$$|$$\\sigma^2$$|\n",
    "|t 분포|$$t=\\frac{\\bar{X} - \\mu}{s/\\sqrt{n}}$$<br/>$$\\bar{X}: \\text{표본 평균}$$<br/>$$\\mu: \\text{모평균}, s: \\text{표본분산}$$|$$\\nu: \\text{자유도}$$|$$\\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\sqrt{\\pi \\nu} \\Gamma\\left(\\frac{\\nu}{2}\\right)} \\left(1 + \\frac{t^2}{\\nu}\\right)^{-\\frac{\\nu + 1}{2}}$$|0, $$\\nu > 1$$|$$\\frac{\\nu}{\\nu-2}, \\nu > 2$$|\n",
    "|카이 제곱(Chi-Square)|표준 정규 분포를 따르는 k개의 독립인 확률 변수의 제곱의 합 분포|k: 자유도|$$\\frac{1}{2^{k/2}\\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}$$|k|2k|\n",
    "|F 분포|두 개의 카이 제곱 분포를 따르는 확률 변수의 비율|d1: 분자의 자유도 d2: 분모의 자유도|별도 기재|$$\\frac{d_{2}}{d_{2}-2}$$,<br/>$$d_2 > 2$$|$$\\frac{2\\,d_{2}^{2}\\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}$$, <br/> $$d2 > 4$$|\n",
    "\n",
    "F 분포의 확률 밀도 함수: $$\\frac{\\Gamma\\left(\\frac{d_1 + d_2}{2}\\right)}{\\Gamma\\left(\\frac{d_1}{2}\\right)\\Gamma\\left(\\frac{d_2}{2}\\right)} \\left(\\frac{d_1}{d_2}\\right)^{d_1/2} \\frac{x^{d_1/2 - 1}}{\\left(1 + \\frac{d_1}{d_2}x\\right)^{\\frac{d_1 + d_2}{2}}}$$\n",
    "\n",
    "\n",
    "#### 자유도의 직관적 이해\n",
    "\n",
    "- 주어진 확률 변수 중에서 임의로 변경이 가능한 값의 수입니다.\n",
    "\n",
    "<div style=\"border: 0px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "예] 표본 분산: $S = \\sum_{i=1}^n\\frac{(X_i - \\bar{X})^2}{n - 1}$, ← 표본 분산의 분모(자유도)가 1 차감이 됩니다.\n",
    "\n",
    "$\\bar{X}=\\frac{X_1 + X_2 + ... + X_n}{n}$ 표본 분산을 구할 때 표본평균을 사용합니다.\n",
    "\n",
    "표본 분산을 구하는 과정에서 표본 평균이 고정이 됩니다. $X_1, ... X_n$ 변수중에서 하나의 값은 값이 고정이 됩니다.\n",
    "\n",
    "n개의 확률 변수에서 한 개가 고정이 되므로 자유도가 n - 1이 됩니다.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f39fb86e",
   "metadata": {},
   "source": [
    "#### scipy.stats\n",
    "\n",
    "- 확률 관련 메소드(method) 정리\n",
    "\n",
    "|메소드명|메소드명 기능|설명|\n",
    "|---|---|---|\n",
    "|rvs|random variates|확률 변수를 생성|\n",
    "|pdf|probability density function|확률 밀도 함수|\n",
    "|pmf|probability mass function|확률 질량 함수|\n",
    "|cdf|cumulative density function|누적 밀도 함수|\n",
    "|ppf|percent point function, inverse of cdf|백분위 함수, cdf의 역함수: 0~1사이의 분위의 역함수|\n",
    "|sf|survival function, 1 - cdf|1 - cdf|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d59c43d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom, poisson, chi2, f, t, norm, expon, gamma"
   ]
  },
  {
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   "id": "fe8b8e1b",
   "metadata": {},
   "source": [
    "**[Ex.1]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "n = 100, p = 0.3 인 이항분포에서 서로 독립인 표본 500개를 만들어 봅니다.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "908a0449",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "표본의 평균: 29.924 모집단(이론적) 평균: 30.0\n",
      "표본의 분산: 21.569362725450905 모집단(이론적) 분산: 21.0\n"
     ]
    },
    {
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Nb34Df39/LFq0CIMHD77viNndGLaIWkKubLa51qGblQohIupcysvLodPpxIderzfbr6amBjk5OYiMjBS3OTg4IDIyEpmZmWZfk5mZadIfAKKjo036jxo1Cnv37sW1a9cgCAK+/vprXLhwAVFRUS1+DwxbRC2hUBlvIG1GXc/xyLxUbeWCiIg6h5CQECiVSvGRlJRktl9JSQnq6+uhUqlMtqtUKmg0GrOv0Wg09+2/efNmhISEoHfv3pDL5ZgwYQJSUlLw61//usXvgVcjErWEwhMIf6/RJHlBFYWzLnH4MOMKuqgflrBAIiL7lJeXh169eonPFQqFVb/+5s2bkZWVhb1796Jv37745ptvEBsbC19f30ajYk1h2CJqKbc+wOj0u9bZUqK4DPhVcBhGxW9BF6nrIyKyQ926dYO7u/t9+3l5ecHR0RFardZku1arbfJm12q1utn+VVVVePnll7F7925MmjQJADBo0CCcOXMGf//731sctngakag1FJ6AexDgFQ64B+HajUpUVFRIXRURUacnl8sxbNgwZGRkiNsMBgMyMjIQERFh9jUREREm/QHg0KFDYv/a2lrU1tbCwcE0Ljk6OsJgMLS4No5sERERkV1ISEhATEwMwsLCMGLECCQnJ6OiogJz584FAMyZMwe9evUS530tWbIEY8eOxfr16zFp0iSkp6fj1KlT2LZtGwDA3d0dY8eOxbJly+Dq6oq+ffvi6NGj+PDDD7Fhw4YW18WwRSSFe277A4W3cdSMiIjabMaMGbhx4wZWrVoFjUaD0NBQ7N+/X5wEX1hYaDJKNWrUKKSlpWHFihV4+eWXERgYiD179mDAgAFin/T0dCxfvhyzZs3Czz//jL59+2Lt2rX405/+1OK6GLaIrM3MbX+gjjJOwHfrI11dRER2IC4uDnFxcWbbjhw50mjb9OnTMX369Cb3p1arsXPnzgeqiXO2iKypidv+QHPQuF1/S5q6iIjIYhi2iKypmdv+QHPQ2E5ERHaFYYvImu5z25/7thMRUYfDsEVkTfe57c9924mIqMNh2CKypmZu+wN1lLGdiIjsCsMWkTU13Pbn3sDVcDUil38gIrI7XPqByNrM3PYHChWDFhGRnWLYIpKCwpPhioiok+BpRCIiIiIL4sgWkQQKCwtRUlJits3Lywt+fn5WroiIiCyFYYvIygoLCxEUFIyqqkqz7a6uXXD+fD4DFxGRnWDYIrKykpISVFVVInxeItx9/E3adEWXkb1jNUpKShi2iIjsBMMWkUTcffzR3a+f1GUQEZGFcYI8ERERkQUxbBERERFZkKRhy9/fHzKZrNEjNjYWAFBdXY3Y2Fj06NEDXbt2xbRp06DVaqUsmYiIiKhVJA1bJ0+eRFFRkfg4dOgQAGD69OkAgKVLl+Lzzz/Hrl27cPToUVy/fh1Tp06VsmQiIiKiVpF0gnzPnj1Nnq9btw4PP/wwxo4di7KyMmzfvh1paWkYN24cAGDnzp0IDg5GVlYWRo4cKUXJRERERK1iM3O2ampq8NFHH2HevHmQyWTIyclBbW0tIiMjxT5BQUHw8/NDZmZmk/vR6/XQ6XTio7y83BrlExEREZllM2Frz549KC0txbPPPgsA0Gg0kMvl8PDwMOmnUqmg0Wia3E9SUhKUSqX4CAkJsWDVRERERM2zmbC1fft2TJw4Eb6+vg+0n+XLl6OsrEx85OXltVOF1OnobwG680BJNqArMD4nIiJqJZtY1PTKlSs4fPgwPvvsM3GbWq1GTU0NSktLTUa3tFot1Gp1k/tSKBRQKBTic51OZ5Gayc5VXAWyFwCag3e2qaOA8PcAtz7S1UVERB2OTYxs7dy5E97e3pg0aZK4bdiwYXB2dkZGRoa4raCgAIWFhYiIiJCiTOos9LcaBy3A+Dx7AUe4iIioVSQf2TIYDNi5cydiYmLg5HSnHKVSifnz5yMhIQHdu3eHu7s7Fi9ejIiICF6JSJal1zYOWg00B43tCk/r1kRERB2W5GHr8OHDKCwsxLx58xq1vf3223BwcMC0adOg1+sRHR2Nd955R4IqqVOpKXuwdiIiortIHraioqIgCILZNhcXF6SkpCAlJcXKVVGnJlc+WDsREdFdbGLOFpFNUaiMk+HNUUcZ24mIiFqIYYvoXgpP41WH9wauhqsROV+LiIhaQfLTiEQ2ya0PMDrdOBm+psx46lChYtAiIqJWY9giaorCk+GKiIgeGE8jEhEREVkQR7aI7lJYWIiSkpJG2728vODn5ydBRURE1NExbBH9orCwEEFBwaiqqmzU5uraBefP5zNwERFRqzFsEf2ipKQEVVWVCJ+XCHcff3G7rugysnesRklJiUXClsLJAdMHdUWYqhYONX7QTd2Hbj27tPvXISIiaTBsEd3D3ccf3f36WeVrKZwcsDpSiT4Xl8DxgvEWQd4AhFtRQHfe9JqIyB5wgjyRhKYP6moMWlrTezHKtLzpNRGRvWDYIpJQmKq2UdASNdz0moiIOjSGLSIJOdXrmu/Am14TEXV4DFtEEqpzdG++A296TUTU4TFsEUnolNYZ9Sre9JqIyJ4xbBFJaNf3t3E1cGOjwCWoeNNrIiJ7waUfiCSkrzMg8XAZpg/agLBHa+FQ8zPKSivh7v0IVFz2gYjILnBki0hi+joDPsrVIf7LKszeWYhHwybj2o3Gq9gTEVHHxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEEMW0REREQWxLBFREREZEGSh61r165h9uzZ6NGjB1xdXTFw4ECcOnVKbBcEAatWrYKPjw9cXV0RGRmJixcvSlgxERERUctJGrZu3bqF0aNHw9nZGV9++SXy8vKwfv16eHp6in3efPNNbNq0CampqcjOzoabmxuio6NRXV0tYeVERERELeMk5Rd/44030KdPH+zcuVPcFhAQIP5dEAQkJydjxYoVePLJJwEAH374IVQqFfbs2YOnn37a6jUTERERtYakI1t79+5FWFgYpk+fDm9vbwwZMgTvvvuu2H7p0iVoNBpERkaK25RKJcLDw5GZmWl2n3q9HjqdTnyUl5db/H2QfejVswsunPocH831Q/JEV8we6g6Fk+Rn2omIqIOT9JPkP//5D7Zu3YrAwEAcOHAAzz33HJ5//nl88MEHAACNRgMAUKlUJq9TqVRi272SkpKgVCrFR0hIiGXfBNmHiqvwvrAEgQWT4Z09Hur/G4KJZQlYHamEi1zSAWAiIurgJA1bBoMBQ4cOxd/+9jcMGTIEixYtwsKFC5GamtrmfS5fvhxlZWXiIy8vrx0rJrukvwVkL4BMe9Bks6P2IPpcXII5Y/pKVBgREdkDScOWj49Po5Gn4OBgFBYWAgDUajUAQKvVmvTRarVi270UCgXc3d3FR7du3SxQOdkVvRbQHDTb5Kg9iIgAFysXRERE9kTSsDV69GgUFBSYbLtw4QL69jWOJAQEBECtViMjI0Ns1+l0yM7ORkREhFVrJTtWU9Zss7OB8/6IiKjtJA1bS5cuRVZWFv72t7/hxx9/RFpaGrZt24bY2FgAgEwmQ3x8PF5//XXs3bsXZ8+exZw5c+Dr64spU6ZIWTrZE7my2eZaB46OEhF1FCkpKfD394eLiwvCw8Nx4sSJZvvv2rULQUFBcHFxwcCBA/HFF1806pOfn48nnngCSqUSbm5uGD58uHgWriUkDVvDhw/H7t278cknn2DAgAF47bXXkJycjFmzZol9XnjhBSxevBiLFi3C8OHDcfv2bezfvx8uLjy1Q+1EoQLUUWab6lVRyLzENd2IiDqCTz/9FAkJCUhMTERubi4GDx6M6OhoFBcXm+1//PhxzJw5E/Pnz8fp06cxZcoUTJkyBefOnRP7/Pvf/8aYMWMQFBSEI0eO4Pvvv8fKlStblUMkv6798ccfx9mzZ1FdXY38/HwsXLjQpF0mk2HNmjXQaDSorq7G4cOH8eijj0pULdklhScQ/h4ElWngqldFoTBwEz48dkWiwoiIqDU2bNiAhQsXYu7cuQgJCUFqaiq6dOmCHTt2mO2/ceNGTJgwAcuWLUNwcDBee+01DB06FFu2bBH7vPLKK/jd736HN998E0OGDMHDDz+MJ554At7e3i2uS/KwRWQT3Pqg+NGNuNjvcxSHZ0Dzq9P4UrkBrx4uRXVNndTVERF1WuXl5SbrZ+r1erP9ampqkJOTY7I2p4ODAyIjI5tcmzMzM9OkPwBER0eL/Q0GA/71r3/h0UcfRXR0NLy9vREeHo49e/a06j0wbBH94tqNSjwaNhmzdxYi/ssqfJSrg77OIHVZRESdWkhIiMn6mUlJSWb7lZSUoL6+vlVrc2o0mmb7FxcX4/bt21i3bh0mTJiAgwcP4qmnnsLUqVNx9OjRFr8HrtZIRERENisvLw+9evUSnysUCqt9bYPB+Av3k08+iaVLlwIAQkNDcfz4caSmpmLs2LEt2g/DFhEREdmsbt26wd3d/b79vLy84Ojo2Kq1OdVqdbP9vby84OTkZHZN0GPHjrX4PfA0IhEREXV4crkcw4YNM1mb02AwICMjo8m1OSMiIkz6A8ChQ4fE/nK5HMOHD292TdCW4MgWkQ1ycHAw3kZIrzUuuir3ABTexisniYjIrISEBMTExCAsLAwjRoxAcnIyKioqMHfuXADAnDlz0KtXL3He15IlSzB27FisX78ekyZNQnp6Ok6dOoVt27aJ+1y2bBlmzJiBX//613jsscewf/9+fP755zhy5EiL62LYIrIxbm5ueLS3K/Dt06a3EVJHAeHvAW59pCuOiMiGzZgxAzdu3MCqVaug0WgQGhqK/fv3i5PgCwsLjb/M/mLUqFFIS0vDihUr8PLLLyMwMBB79uzBgAEDxD5PPfUUUlNTkZSUhOeffx79+vXD//t//w9jxoxpcV0MW0Q2ZvUr8XD97nngnhtjQ3MQyF4AjE7nCBcRURPi4uIQFxdnts3caNT06dMxffr0Zvc5b948zJs3r801cc4WkY15ImokZPcGrQaag8ZTi0RE1GEwbBHZGIXDfW4PdJ8bZxMRkW1h2CKyMXrDfe63dZ8bZxMRkW1h2CKyMXsPZjW6T6NIHWW8cTYREXUYDFtENiZxbTKqBm8yBqu7NVyNyMnxREQdCq9GJLIxFRUVuPBTFUJHp9+1zpbSOKLFoEVE1OEwbBHZIIPBYAxWDFdERB0eTyMSERERWRDDFhEREZEFMWwRERERWRDDFhEREZEFMWwRERERWRDDFhEREZEFMWwRERERWRDX2SJqofz8/BZtIyIiuhvDFtF9VJXdBCDD7Nmzm+xTq6+xXkFERNShMGwR3UdtZTkAAaF/eBE9A4JM2orOZuLc3m2oq6uTpjgiIrJ5DFtELdTV2w/d/fqZbNMVXZamGCIi6jA4QZ6IiIjIghi2iIiIiCyIYYuIiIjIghi2iIiIiCyIYYuIiIjIgiQNW6+++ipkMpnJIyjozqX11dXViI2NRY8ePdC1a1dMmzYNWq1WwoqJiIiIWkfyka3+/fujqKhIfBw7dkxsW7p0KT7//HPs2rULR48exfXr1zF16lQJqyUiIiJqHcnX2XJycoJarW60vaysDNu3b0daWhrGjRsHANi5cyeCg4ORlZWFkSNHWrtUIiIiolaTfGTr4sWL8PX1xUMPPYRZs2ahsLAQAJCTk4Pa2lpERkaKfYOCguDn54fMzEypyiUiIiJqFUlHtsLDw/H++++jX79+KCoqwurVq/GrX/0K586dg0ajgVwuh4eHh8lrVCoVNBpNk/vU6/XQ6/Xi8/LyckuVT0RERHRfkoatiRMnin8fNGgQwsPD0bdvX/zjH/+Aq6trm/aZlJSE1atXt1eJRERERA9E8tOId/Pw8MCjjz6KH3/8EWq1GjU1NSgtLTXpo9Vqzc7xarB8+XKUlZWJj7y8PAtXTURERNQ0mwpbt2/fxr///W/4+Phg2LBhcHZ2RkZGhtheUFCAwsJCRERENLkPhUIBd3d38dGtWzdrlE4djf4WoDsPlGQDugJAfwsODjb1z4GIiOyEpKcR//rXv2Ly5Mno27cvrl+/jsTERDg6OmLmzJlQKpWYP38+EhIS0L17d7i7u2Px4sWIiIjglYj0YCquAtkLAM3BO9vUUXh00Ca4ublJVxcREdklScPWTz/9hJkzZ+LmzZvo2bMnxowZg6ysLPTs2RMA8Pbbb8PBwQHTpk2DXq9HdHQ03nnnHSlLpo5Of6tx0AIAzUG4Cs9j9SvxOFAhTWlERGSfJA1b6enpzba7uLggJSUFKSkpVqqI7J5e2zho/UKmPYgnohbjwO4SKxdFRET2jJNUqHOpKWu2WeFQbaVCiIios2DYos5Frmy2WW9wsVIhRETUWTBsUeeiUAHqKLNNgioKew9mWbkgIiKydwxb1LkoPIHw9xoHLnUUqgZvRuLaZEnKIiIi+yX5jaiJrM6tDzA63ThZvqbMeGpRocKF/CuoqOCliERE1L7aNLL10EMP4ebNm422l5aW4qGHHnrgoogsTuEJuAcBXuHGPxWeMBgMUldFRER2qE0jW5cvX0Z9fX2j7Xq9HteuXXvgoojIDP2tu0bjPACFtzE0EhGRTWtV2Nq7d6/49wMHDkCpvHNlV319PTIyMuDv799uxRHRL5pY9R7h7xlPixIRkc1qVdiaMmUKAEAmkyEmJsakzdnZGf7+/li/fn27FUdEaHbVe2QvMM4/4wgXEZHNalXYapjTEhAQgJMnT8LLy8siRRHRXZpZ9R6ag8Z2hi0iIpvVpjlbly5dau86iKgp91n1/r7tREQkqTYv/ZCRkYGMjAwUFxc3uoprx44dD1wYEf3iPqve37ediIgk1aalH1avXo2oqChkZGSgpKQEt27dMnkQUTtqZtV7qKOM7UREZLPaNLKVmpqK999/H88880x710NE92pY9b6pqxE5X4uIyKa1KWzV1NRg1KhR7V0LkV3Kz89v9nmLNLHqPYMWEZHta1PYWrBgAdLS0rBy5cr2rofIblSV3QQgw+zZs8221+prWrdDhSfDFRFRB9SmsFVdXY1t27bh8OHDGDRoEJydnU3aN2zY0C7FEXVktZXlAASE/uFF9AwIErcXnc3Eub3bUFdXJ11xRERkNW0KW99//z1CQ0MBAOfOnTNpk8lkD1wUkT3p6u2H7n79xOe6osvSFUNERFbXprD19ddft3cdRERERHapTUs/EBEREVHLtGlk67HHHmv2dOFXX33V5oKIiIiI7EmbwlbDfK0GtbW1OHPmDM6dO9foBtVEREREnVmbwtbbb79tdvurr76K27dvP1BBRERERPakXedszZ49m/dFJCIiIrpLu4atzMxMuLi4tOcuiYiIiDq0Np1GnDp1qslzQRBQVFSEU6dOcVV5IiIioru0KWwplUqT5w4ODujXrx/WrFmDqKiodimMiIiIyB60KWzt3LmzvesgohYoLCxESUlJo+1eXl7w8/OToCIiIrqfNoWtBjk5OcjPzwcA9O/fH0OGDGmXooioscLCQgQFBaOqqrJRm6trF5w/n8/ARURkg9oUtoqLi/H000/jyJEj8PDwAACUlpbiscceQ3p6Onr27NmeNRIRgJKSElRVVSJ8XiLcffzF7bqiy8jesRolJSUMW0RENqhNVyMuXrwY5eXl+OGHH/Dzzz/j559/xrlz56DT6fD888+3d41EdBd3H3909+snPu4OXkREZHvaNLK1f/9+HD58GMHBweK2kJAQpKSkcII8ERER0V3aNLJlMBjg7OzcaLuzszMMBkObClm3bh1kMhni4+PFbdXV1YiNjUWPHj3QtWtXTJs2DVqttk37JyIiIvuXkpICf39/uLi4IDw8HCdOnGi2/65duxAUFAQXFxcMHDgQX3zxRZN9//SnP0EmkyE5OblVNbUpbI0bNw5LlizB9evXxW3Xrl3D0qVLMX78+Fbv7+TJk/jv//5vDBo0yGT70qVL8fnnn2PXrl04evQorl+/3miNLyIiIiIA+PTTT5GQkIDExETk5uZi8ODBiI6ORnFxsdn+x48fx8yZMzF//nycPn0aU6ZMwZQpU3Du3LlGfXfv3o2srCz4+vq2uq42ha0tW7ZAp9PB398fDz/8MB5++GEEBARAp9Nh8+bNrdrX7du3MWvWLLz77rvw9PQUt5eVlWH79u3YsGEDxo0bh2HDhmHnzp04fvw4srKy2lI2ERER2bENGzZg4cKFmDt3LkJCQpCamoouXbo0eSvBjRs3YsKECVi2bBmCg4Px2muvYejQodiyZYtJv2vXrmHx4sX4+OOPzZ7Zu582ha0+ffogNzcX//rXvxAfH4/4+Hh88cUXyM3NRe/evVu1r9jYWEyaNAmRkZEm23NyclBbW2uyPSgoCH5+fsjMzGxL2URERGSnampqkJOTY5IbHBwcEBkZ2WRuyMzMbJQ/oqOjTfobDAY888wzWLZsGfr379+m2lo1Qf6rr75CXFwcsrKy4O7ujt/+9rf47W9/C8A4EtW/f3+kpqbiV7/6VYv2l56ejtzcXJw8ebJRm0ajgVwuF5eWaKBSqaDRaJrcp16vh16vF5+Xl5e3qBYiIiKyPeXl5dDpdOJzhUIBhULRqF9JSQnq6+uhUqlMtqtUKpw/f97svjUajdn+d+eMN954A05OTg+02kKrRraSk5OxcOFCuLu7N2pTKpX44x//iA0bNrRoX1evXsWSJUvw8ccft+vNq5OSkqBUKsVHSEhIu+2biIiIrCskJMTkcz0pKclqXzsnJwcbN27E+++/D5lM1ub9tCpsfffdd5gwYUKT7VFRUcjJyWnRvnJyclBcXIyhQ4fCyckJTk5OOHr0KDZt2gQnJyeoVCrU1NSgtLTU5HVarRZqtbrJ/S5fvhxlZWXiIy8vr0X1EBERke3Jy8sz+Vxfvny52X5eXl5wdHRstGpBc7lBrVY32////u//UFxcDD8/PzGrXLlyBX/5y1/g7+/f4vfQqrCl1WqbnRjm5OSEGzdutGhf48ePx9mzZ3HmzBnxERYWhlmzZol/d3Z2RkZGhviagoICFBYWIiIiosn9KhQKuLu7i49u3bq1/A0SERGRTenWrZvJ57q5U4gAIJfLMWzYMJPcYDAYkJGR0WRuiIiIMOkPAIcOHRL7P/PMM/j+++9Nsoqvry+WLVuGAwcOtPg9tGrOVq9evXDu3Dk88sgjZtu///57+Pj4tGhf3bp1w4ABA0y2ubm5oUePHuL2+fPnIyEhAd27d4e7uzsWL16MiIgIjBw5sjVlEwH6W4BeC9SUAXIPQOENKDzv+zIiIuo4EhISEBMTg7CwMIwYMQLJycmoqKjA3LlzAQBz5sxBr169xFORS5YswdixY7F+/XpMmjQJ6enpOHXqFLZt2wYA6NGjB3r06GHyNZydnaFWq9GvX78W19WqsPW73/0OK1euxIQJExrNs6qqqkJiYiIef/zx1uyyWW+//TYcHBwwbdo06PV6REdH45133mm3/VMnUXEVyF4AaA7e2aaOAsLfA9z6SFcXERG1qxkzZuDGjRtYtWoVNBoNQkNDsX//fnESfGFhIRwc7pzUGzVqFNLS0rBixQq8/PLLCAwMxJ49exoNBj2oVoWtFStW4LPPPsOjjz6KuLg4MdWdP38eKSkpqK+vxyuvvNLmYo4cOWLy3MXFBSkpKUhJSWnzPqmT099qHLQA4/PsBcDodI5wERHZkbi4OMTFxZltuzdnAMD06dMxffr0Fu//8uXLra6pVWFLpVLh+PHjeO6557B8+XIIggAAkMlkiI6ORkpKSqNLKIkkpdc2DloNNAeN7QxbRERkQa2+EXXfvn3xxRdf4NatW/jxxx8hCAICAwNNVn8nshk1ZQ/WTkRE9IBaHbYaeHp6Yvjw4e1ZC1H7kysfrJ2IiOgBtel2PUQdhkJlnAxvjjrK2E5ERGRBDFtk3xSexqsO7w1cDVcjduD5WgonB8we6o6d8/vjSu4uhPRxMl4QQERENqXNpxGJOgy3PsarDsV1tpTGEa0OHrRWRyrR5+ISOF745QKAfHBJCyIiG8SwRZ2DwrNDh6t7TR/U1Ri0tFzSgojI1vE0IlEHFKaqbRy0GjQsaUFERDaBYYuoA3Kq1zXfgUtaEBHZDIYtog6oztG9+Q5c0oKIyGYwbBF1QKe0zqhXcUkLIqKOgGGLqAPa9f1tXA3c2Dhw2cGSFkRE9oZXIxJ1QPo6AxIPl2H6oA0Y8lAl6kuvwLtXIFyUfgxaREQ2hiNbRB2Uvs6Aj3J1mLv9B/QdOh15P9UzaBER2SCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiCGLSIiIiILYtgiIiIisiBJw9bWrVsxaNAguLu7w93dHREREfjyyy/F9urqasTGxqJHjx7o2rUrpk2bBq1WK2HFRERERK0jadjq3bs31q1bh5ycHJw6dQrjxo3Dk08+iR9++AEAsHTpUnz++efYtWsXjh49iuvXr2Pq1KlSlkxERETUKk5SfvHJkyebPF+7di22bt2KrKws9O7dG9u3b0daWhrGjRsHANi5cyeCg4ORlZWFkSNHSlEyERERUatIGrbuVl9fj127dqGiogIRERHIyclBbW0tIiMjxT5BQUHw8/NDZmZmk2FLr9dDr9eLz8vLyy1eO9mmwsJClJSUNNru5eUFPz8/CSoiIqLOSPKwdfbsWURERKC6uhpdu3bF7t27ERISgjNnzkAul8PDw8Okv0qlgkajaXJ/SUlJWL16tYWrJltXWFiIoKBgVFVVNmpzde2C8+fzGbiIiMgqJA9b/fr1w5kzZ1BWVob//d//RUxMDI4ePdrm/S1fvhwJCQni82vXriEkJKQ9SqWOQn8L3i63cP7bDyDr1gvZhXX48NgVVNfUQVd0Gdk7VqOkpIRhi4iIrELysCWXy/HII48AAIYNG4aTJ09i48aNmDFjBmpqalBaWmoyuqXVaqFWq5vcn0KhgEKhEJ/rdDqL1U42qOIqkL0ALpqDaIhSvqoohD27EYmHyyQtjYiIOiebW2fLYDBAr9dj2LBhcHZ2RkZGhthWUFCAwsJCRERESFgh2Sz9LSB7AaA5aLLZUXsQfS4uwfRBXSUqjIiIOjNJR7aWL1+OiRMnws/PD+Xl5UhLS8ORI0dw4MABKJVKzJ8/HwkJCejevTvc3d2xePFiRERE8EpEMk+vbRS0GjhqDyLs0VorF0RERCRx2CouLsacOXNQVFQEpVKJQYMG4cCBA/jtb38LAHj77bfh4OCAadOmQa/XIzo6Gu+8846UJZMtq2n+NKFTvX1fmerg4GAc3dNrjcdC7gEovAGFp9SlERF1apKGre3btzfb7uLigpSUFKSkpFipIurQ5Mpmm+scu1mpEOtzc3PDo71dgW+fNh3dU0cB4e8Bbn2kK46IqJOzuTlbRG2mUBnDhRn1qiic0jpbuSDrWf1KPFy/e77xaVTNQeM8Nv0taQojIiKGLbIjCk/jKM49gateFYXCwE3Y9f1tiQqzvCeiRkKmNT9fDZqDxlOLREQkCcmXfiBqV259gNHpqC4rRPG1i3D06IvTN7tg1+FS6OsMUldnMQqH6uY73Gc+GxERWQ5Htsj+KDyR91M9+g6djrnbf8BHuTq7DloAoDe4NN/hPvPZiIjIchi2iOzA3oNZEFTm56tBHWWcz0ZERJJg2CKyA4lrk1E1eFPjCwQarkbk8g9ERJLhnC0iO1BRUYELP1UhdHT6XetsKY0jWgxaRESSYtgishMGg8EYrBiuiIhsCk8jEhEREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsEREREVkQwxYRERGRBTFsERERkd1ISUmBv78/XFxcEB4ejhMnTjTbf9euXQgKCoKLiwsGDhyIL774Qmyrra3Fiy++iIEDB8LNzQ2+vr6YM2cOrl+/3qqaGLaIiIjILnz66adISEhAYmIicnNzMXjwYERHR6O4uNhs/+PHj2PmzJmYP38+Tp8+jSlTpmDKlCk4d+4cAKCyshK5ublYuXIlcnNz8dlnn6GgoABPPPFEq+pi2CIiIiK7sGHDBixcuBBz585FSEgIUlNT0aVLF+zYscNs/40bN2LChAlYtmwZgoOD8dprr2Ho0KHYsmULAECpVOLQoUP4/e9/j379+mHkyJHYsmULcnJyUFhY2OK6GLaIiIjIZpWXl0On04kPvV5vtl9NTQ1ycnIQGRkpbnNwcEBkZCQyMzPNviYzM9OkPwBER0c32R8AysrKIJPJ4OHh0eL3wLBFHZ/+FqA7D5RkA7oCQH8LDg780RaZOT5ERB1FSEgIlEql+EhKSjLbr6SkBPX19VCpVCbbVSoVNBqN2ddoNJpW9a+ursaLL76ImTNnwt3dvcXvwanFPYlsUcVVIHsBoDl4Z5s6Co8O2gQ3Nzfp6rIVTRwfhL8HuPWRri4iohbKy8tDr169xOcKhUKSOmpra/H73/8egiBg69atrXotf/2njkt/q3GQAADNQbh+9zxWvxIvSVk2o5njg+wFHOEiog6hW7ducHd3Fx9NhS0vLy84OjpCq9WabNdqtVCr1WZfo1arW9S/IWhduXIFhw4datWoFsCwRR2ZXts4SPxCpj2IJ6JGWrmg9pOfn4/c3FyTR35+fut20szxgeagsZ2IyE7I5XIMGzYMGRkZ4jaDwYCMjAxERESYfU1ERIRJfwA4dOiQSf+GoHXx4kUcPnwYPXr0aHVtkp5GTEpKwmeffYbz58/D1dUVo0aNwhtvvIF+/fqJfaqrq/GXv/wF6enp0Ov1iI6OxjvvvNPoHCt1QjVlzTYrHKqtVEj7qSq7CUCG2bNnN9mnVl/Tsp3d5/jct52IqINJSEhATEwMwsLCMGLECCQnJ6OiogJz584FAMyZMwe9evUS530tWbIEY8eOxfr16zFp0iSkp6fj1KlT2LZtGwBj0Pqv//ov5ObmYt++faivrxfnc3Xv3h1yubxFdUkato4ePYrY2FgMHz4cdXV1ePnllxEVFYW8vDxxvs3SpUvxr3/9C7t27YJSqURcXBymTp2Kb7/9VsrSyRbIlc026w0uAG5bp5Z2UltZDkBA6B9eRM+AIJO2orOZOLd3G+rq6lq2s/scn/u2ExF1MDNmzMCNGzewatUqaDQahIaGYv/+/eIATWFhockFVKNGjUJaWhpWrFiBl19+GYGBgdizZw8GDBgAALh27Rr27t0LAAgNDTX5Wl9//TV+85vftKguScPW/v37TZ6///778Pb2Rk5ODn7961+jrKwM27dvR1paGsaNGwcA2LlzJ4KDg5GVlYWRIzvuaSJqBwqVcbK3mVNlgioKew9mAXjE+nW1g67efuju189km67ocut20szxgTrK2E5EZGfi4uIQFxdntu3IkSONtk2fPh3Tp08329/f3x+CIDxwTTY1Z6uszHhao3v37gCAnJwc1NbWmqyBERQUBD8/vybXwNDr9SbrcZSXl1u+cJKGwtN4VZ06ynS7OgpVgzcjcW2yJGXZjGaOD8LfM7YTEZHF2czSDwaDAfHx8Rg9erQ4fKfRaCCXyxstHNbcGhhJSUlYvXq1pcslW+HWBxidbpzsXVNmPDWmUOFC/hVUVFRIXZ30mjg+DFpERNZjM2ErNjYW586dw7Fjxx5oP8uXL0dCQoL4/Nq1awgJCXnQ8siWKTwbhQeD4ZJExdggM8eHiIisxybCVlxcHPbt24dvvvkGvXv3Frer1WrU1NSgtLTUZHSruTUzFAqFyRocOp3OYnUTERER3Y+kc7YEQUBcXBx2796Nr776CgEBASbtw4YNg7Ozs8kaGAUFBSgsLGxyzQwiIiIiWyLpyFZsbCzS0tLwz3/+E926dRPnYSmVSri6ukKpVGL+/PlISEhA9+7d4e7ujsWLFyMiIoJXItIDMbdAaKsXDSUiImoBScNWw72F7l2nYufOnXj22WcBAG+//TYcHBwwbdo0k0VNidqiXRcNJSIiagFJw1ZL1q5wcXFBSkoKUlJSrFAR2bt2XTSUiIioBWxigjyRtbXLoqFEREQtYFOLmhIRERHZG4YtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIK6zRdTZ6G8Bei1QUwbIPQCFN6DwlLoqIiK7xbBF1JlUXAWyFwCag3e2qaOA8PcAtz7S1UVEZMd4GpGos9Dfahy0AOPz7AXGdiIiancc2aKOhafA2k6vbRy0GmgOGtt5LImI2h3DFnUcPAX2YGrKHqydiIjahKcRqWPgKbAHJ1c+WDsREbUJR7aoY+ApsPvKz883u93Lywt+fn6AQmUcCTR3HNVRxnYiImp3DFvUMfAUWJOqym4CkGH27Nlm211du+D8+Xxj4Ap/r+lTsZ08rBIRWQrDFnUMPAXWpNrKcgACQv/wInoGBJm06YouI3vHapSUlBjDllsfYHT6XRcZKI0jWgxaREQWw7BFHQNPgd1XV28/dPfrd/+OCk+GKyIiK+IEeeoYFJ7GU13qKNPtPAVGREQ2jiNb1HHwFBgREXVADFvUsfAUGBERdTA8jUhERERkQQxbRERERBbEsEVERERkQQxbRERERBbEsEVERERkQbwakYiMN/IWl9TwABTevOqTiKidMGwRdXYVV5u+X6JbH+nqIiKyEzyNSNSZ6W81DlqA8Xn2AmM7ERE9EI5skW3j6S3L0mvN328SMG7Xa3m8iYgeEMMW2S6e3rK8mrIHayciovti2CLbdL/TW6PTAYUnCgsLUVJS0ujl+fn5Viq0Y2jqeAzs6wbn5l4oV1qkHiKizkTSsPXNN9/grbfeQk5ODoqKirB7925MmTJFbBcEAYmJiXj33XdRWlqK0aNHY+vWrQgMDJSuaLKOFpzeKtSWIygoGFVVlU3uplZfY6ECO4aqspsAZJg9e7bZ9uQ3E/H8sCjIzB1rdZTxRt9ERPRAJA1bFRUVGDx4MObNm4epU6c2an/zzTexadMmfPDBBwgICMDKlSsRHR2NvLw8uLi4SFAxWU0LTm+VlFSiqqoS4fMS4e7jb9JcdDYT5/ZuQ11dneVq7ABqK8sBCAj9w4voGRBk0qYruoxXVv8dCy/noAueN3+6lvO1iIgemKRha+LEiZg4caLZNkEQkJycjBUrVuDJJ58EAHz44YdQqVTYs2cPnn76aWuWStZ2v9NXciUA44iWu48/uvv1M2nWFV22TF0dVFdvv0bHCDD+wnPhpyqEjk6/60IEpXFEi0GLiKhd2OzSD5cuXYJGo0FkZKS4TalUIjw8HJmZmU2+Tq/XQ6fTiY/y8nJrlEvtTaEyjq6Yw9Nb7cpgMBiDlXsQ4BVu/JNBi4io3dhs2NJoNAAAlcr0Q1WlUolt5iQlJUGpVIqPkJAQi9ZJFqLwNJ7Gujdw8fQWERF1MHZ3NeLy5cuRkJAgPr927RoDV0fl1sd41SFPbxERUQdms2FLrVYDALRaLXx8fMTtWq0WoaGhTb5OoVBAoVCIz3U6ncVqJCtQeDJcSYGLyRIRtRubPY0YEBAAtVqNjIwMcZtOp0N2djYiIiIkrIzIzlVcBb59GtgXDBwcCewLMj6vuCp1ZUREHZKkI1u3b9/Gjz/+KD6/dOkSzpw5g+7du8PPzw/x8fF4/fXXERgYKC794Ovra7IWF9k/LlxqRS1cTJaIiFpO0rB16tQpPPbYY+LzhrlWMTExeP/99/HCCy+goqICixYtQmlpKcaMGYP9+/dzja1OpLCwkAuXWhPvlUhE1O4kDVu/+c1vIAhCk+0ymQxr1qzBmjVrrFgVScbMPKGff/6ZC5daE++VSETU7mx2gjx1Mk3cdPrRQZvg5ubGhUutpUWLyRIRUWvY7AR56kSamSfk+t3zWP1KvCRldUpcTJaIqN0xbJH0mpknJNMexBNRI61cUCfGxWSJiNodTyOS9O4zD0jhUG2lQghA04vJAoDuPNfeIiJqJYYtkt595gHpDS4AblunFjK6dzHZJubUIfw9YzgjIqImMWyR9BrmCZk5lSioorD3YBaAR6xfVydhbr0yLy8v+Pn5GZ9w7S0iogfCsEXSEZd6KAeGpwAnYxuNnFQN2ozEJ4diVPwW6eq0U1VlNwHIMHv27EZtrq5dcP58vjFwce0tIqIHwrBF0rj3tJSTGzDkbWDoeqCuQpwndCH/CioqKqSt1U7VVpYDEBD6hxfRMyBI3K4ruozsHatRUlJiDFtce4uI6IEwbJH1mTstVVcBnFxkPJ1412kpg+GSREV2Hl29/RqtYWbC3Jw6JzegXzzgNRIQagFdASfMExE1gUs/kPW15LQU2Y57195ycgNGfwKUZAFHJwOHfsWbVRMRNYNhi6yPp6U6hPz8fOTm5uJM/hVUDtoEQfVL4OoXD5zfCGgzTF/QMGFef8vqtRIR2TKeRiTruPu+h06uzfflLWEkZW7ivJubG1a/Eo8nohbD31cN5x/WNn6hkxvQYzhQdRUov8C1uIiIfsGwRZZ372T4/q8AqkhAe7hxX94SRnJNTZw/UAHseucU/hE3AH73vqjh1OL5jcDdQYxrcRERMWyRhTSMZBkMQO5S0zlaBcnGD2bANHDxljA2pamJ88ZFZu9h7tRiw0hX+UWg8idA0Z0jXUTUKTFsUfu7eyRr7OeNJ8PXVQDfzjR+QA9bD9RVAXIldDWu+M/FmzAYbohdzS24SdLaezALCSOiINPe9X31Gmk6otXUSFevJ4BhmwBDFW/7Q0SdBsNWW9w9/6jhwwK4a5sn4NQNqCt7wD6W3LeF+ii8gJN/vhOw6pu4r2FdhfFDuNdkwCschYWFCAoKRlVVpdnutfqaVn6TyFIS1ybjucs56PL9801/n5sa6XpkgTGIN4xoNqyv1jPil/XVPGzr55n/vtmHfVrXxwZ+cUpJScFbb70FjUaDwYMHY/PmzRgxYkST/Xft2oWVK1fi8uXLCAwMxBtvvIHf/e53YrsgCEhMTMS7776L0tJSjB49Glu3bkVgYGCLa2LYai1zi3GO3Qf8kGTcJv5Gv8n0A6W1fSy5b0v2uXcky9HMKae7/TIZvqSkBFVVlQiflwh3H3+xuehsJs7t3Ya6urpWfqPIUioqKnDhpyqE3n2z6nsverh3pAtoHMDuHv06uejONlv6eea/b/Zhn5b1AWxijuann36KhIQEpKamIjw8HMnJyYiOjkZBQQG8vb0b9T9+/DhmzpyJpKQkPP7440hLS8OUKVOQm5uLAQMGAADefPNNbNq0CR988AECAgKwcuVKREdHIy8vDy4u9/mM+wWXfmgNc4tx9osHzr1+Z5v4gXL4wfpYct+W7HPvCEdJFqAaD7PMTIZ39/FHd79+4sPNy8f8a0lSBoPB+BusexDgFQ649jFdi8vciKbXSNORLnOjX7b288x/3+zDPi3rA9jE8i8bNmzAwoULMXfuXISEhCA1NRVdunTBjh07zPbfuHEjJkyYgGXLliE4OBivvfYahg4dii1bjLeIEwQBycnJWLFiBZ588kkMGjQIH374Ia5fv449e/a0uC6GrdYwtxjnvR8g9z5vax9L7tuSfe4dySpIBoKWNA5cnAxvXxSexu9nQ+AyN6J5bwCT+mdVyj5Sf332YZ/27tPAAgtTl5eXQ6fTiQ+9Xm+2X01NDXJychAZGSluc3BwQGRkJDIzM82+JjMz06Q/AERHR4v9L126BI1GY9JHqVQiPDy8yX2aw7DVGuYW27z3A8Tcb/Rt6WPJfVuyz70jWQ2T4b1GAuMygKjjwOP5xlvycDkA++LWx/h9fTwfcHvIdKQLaBzApP5ZlbKP1F+ffdinvfvcrZ0Xpg4JCYFSqRQfSUlJZvuVlJSgvr4eKpXpGROVSgWNRmP2NRqNptn+DX+2Zp/mcM5Wa5hbbPPeDxBzv9G3pY8l923JPibLOvzym09dBXDzJPDIHxmw7J3C885oZfh7pqfdS7JM11eT+mdVyj5Sf332YZ/27nO3dl6YOi8vD7169RKfKxSKdt2/NXBkqzXuvUcc0Hgkx9wcpbb0seS+LdmnYSTLbwbwux+AqCyOZHVWd490RWUBAc8A4e/e+Tck9c+qlH2k/vrswz7t3aeBBRam7tatG9zd3cVHU2HLy8sLjo6O0GpNT2NqtVqo1Wrz5arVzfZv+LM1+zSHI1ut0TAv5e7f1guSjVdpyByN28SRHdmd3+Db0seS+7ZkHwDwGg34TmC4ItORrgbiVYzlwEPPAidjO/bPfGf6980+7NPc//0Sz8WVy+UYNmwYMjIyMGXKFADGi3kyMjIQFxdn9jURERHIyMhAfHy8uO3QoUOIiIgAAAQEBECtViMjIwOhoaEAAJ1Oh+zsbDz33HMtro1hq7UaflsX1xpRGlO8yTYPIOLDu9YfaWsfS+7bwn048Z2acm8As5ef+c7075t92MdG/+9PSEhATEwMwsLCMGLECCQnJ6OiogJz584FAMyZMwe9evUS530tWbIEY8eOxfr16zFp0iSkp6fj1KlT2LZtGwBAJpMhPj4er7/+OgIDA8WlH3x9fcVA1xIMW21h7rf1hu0mzCxb0KY+lty3BfsQtYTV/z3ZWh+pvz77sE8795HQjBkzcOPGDaxatQoajQahoaHYv3+/OMG9sLAQDg53ZlCNGjUKaWlpWLFiBV5++WUEBgZiz5494hpbAPDCCy+goqICixYtQmlpKcaMGYP9+/e3eI0tgGGLiIiI7EhcXFyTpw2PHDnSaNv06dMxffr0Jvcnk8mwZs0arFmzps01cYI8ERERkQVxZIusqrCwECUlJY2284bTRERkrxi2yGrud7NpgDecJiIi+8OwRVbT1M2mAd5wmoiI7BfDFlldw82m76YruixNMURERBbGsEVt1tT8Ky8vL/j5+UlQEVlLU3Ps9Hq92dWd+TNBRJ1ZhwhbKSkpeOutt6DRaDB48GBs3rwZI0aMkLqsTq25+Veurl1w/nw+P1ztUFXZTQAyzJ4923wHmQwQhEab+TNBRJ2ZzYetTz/9FAkJCUhNTUV4eDiSk5MRHR2NgoICeHt7S11ep9XU/Ctd0WVk71iNkpISfrDaodrKcgACQv/wInoGBJm0Ncy7u7eNPxNE1NnZfNjasGEDFi5cKC61n5qain/961/YsWMHXnrpJYmrI3Pzr8j+dfX2a3Lenbk2IqLOzKbDVk1NDXJycrB8+XJxm4ODAyIjI5GZmWn2NXq9Hnq9XnxeVlYGACgqKrJssZ1Mwx3Qb1z8HtW6n8Xt5dqfAADHjh1rdJf0ixcvmn0NANwqNLb9fPkcZPXV993e1jZrvYb7u9PW8DOh1Wrx008/gYioJRo+tw0Gg8SVtAPBhl27dk0AIBw/ftxk+7Jly4QRI0aYfU1iYqIAgA8++OCDDz74sIPHiRMnrBE5LMqmR7baYvny5UhISBCf19XVIT8/H3369DG5+eSDKi8vR0hICPLy8tCtW7d22y81xmNtHTzO1sHjbB08ztZhyeNsMBig1WoxZMiQdt2vFGw6bHl5ecHR0bHR6SitVgu1Wm32NQqFotGl56NHj2732nQ6HQCgV69ecHd3b/f90x081tbB42wdPM7WweNsHZY+zvZyUY1N34haLpdj2LBhyMjIELcZDAZkZGQgIiJCwsqIiIiIWsamR7YAICEhATExMQgLC8OIESOQnJyMiooK8epEIiIiIltm82FrxowZuHHjBlatWgWNRoPQ0FDs378fKpVK0roUCgUSExPNrpZN7YvH2jp4nK2Dx9k6eJytg8e5ZWSCYGa5ZyIiIiJqFzY9Z4uIiIioo2PYIiIiIrIghi0iIiIiC2LYIiIiIrIghq02SklJgb+/P1xcXBAeHo4TJ05IXVKHlpSUhOHDh6Nbt27w9vbGlClTUFBQYNKnuroasbGx6NGjB7p27Ypp06Y1WvCWWmfdunWQyWSIj48Xt/E4t49r165h9uzZ6NGjB1xdXTFw4ECcOnVKbBcEAatWrYKPjw9cXV0RGRkp3j+UWqa+vh4rV65EQEAAXF1d8fDDD+O1117D3dd98Ti3zTfffIPJkyfD19cXMpkMe/bsMWlvyXH9+eefMWvWLLi7u8PDwwPz58/H7du3rfgubAfDVht8+umnSEhIQGJiInJzczF48GBER0ejuLhY6tI6rKNHjyI2NhZZWVk4dOgQamtrERUVhYqKCrHP0qVL8fnnn2PXrl04evQorl+/jqlTp0pYdcd28uRJ/Pd//zcGDRpksp3H+cHdunULo0ePhrOzM7788kvk5eVh/fr18PT0FPu8+eab2LRpE1JTU5GdnQ03NzdER0ejurq6mT3T3d544w1s3boVW7ZsQX5+Pt544w28+eab2Lx5s9iHx7ltKioqMHjwYKSkpJhtb8lxnTVrFn744QccOnQI+/btwzfffINFixZZ6y3YFilvzNhRjRgxQoiNjRWf19fXC76+vkJSUpKEVdmX4uJiAYBw9OhRQRAEobS0VHB2dhZ27dol9snPzxcACJmZmVKV2WGVl5cLgYGBwqFDh4SxY8cKS5YsEQSBx7m9vPjii8KYMWOabDcYDIJarRbeeustcVtpaamgUCiETz75xBol2oVJkyYJ8+bNM9k2depUYdasWYIg8Di3FwDC7t27xectOa55eXkCAOHkyZNiny+//FKQyWTCtWvXrFa7reDIVivV1NQgJycHkZGR4jYHBwdERkYiMzNTwsrsS1lZGQCge/fuAICcnBzU1taaHPegoCD4+fnxuLdBbGwsJk2aZHI8AR7n9rJ3716EhYVh+vTp8Pb2xpAhQ/Duu++K7ZcuXYJGozE5zkqlEuHh4TzOrTBq1ChkZGTgwoULAIDvvvsOx44dw8SJEwHwOFtKS45rZmYmPDw8EBYWJvaJjIyEg4MDsrOzrV6z1Gx+BXlbU1JSgvr6+kYr2KtUKpw/f16iquyLwWBAfHw8Ro8ejQEDBgAANBoN5HI5PDw8TPqqVCpoNBoJquy40tPTkZubi5MnTzZq43FuH//5z3+wdetWJCQk4OWXX8bJkyfx/PPPQy6XIyYmRjyW5v4f4XFuuZdeegk6nQ5BQUFwdHREfX091q5di1mzZgEAj7OFtOS4ajQaeHt7m7Q7OTmhe/funfLYM2yRzYmNjcW5c+dw7NgxqUuxO1evXsWSJUtw6NAhuLi4SF2O3TIYDAgLC8Pf/vY3AMCQIUNw7tw5pKamIiYmRuLq7Mc//vEPfPzxx0hLS0P//v1x5swZxMfHw9fXl8eZbApPI7aSl5cXHB0dG12dpdVqoVarJarKfsTFxWHfvn34+uuv0bt3b3G7Wq1GTU0NSktLTfrzuLdOTk4OiouLMXToUDg5OcHJyQlHjx7Fpk2b4OTkBJVKxePcDnx8fBASEmKyLTg4GIWFhQAgHkv+P/Jgli1bhpdeeglPP/00Bg4ciGeeeQZLly5FUlISAB5nS2nJcVWr1Y0uGqurq8PPP//cKY89w1YryeVyDBs2DBkZGeI2g8GAjIwMRERESFhZxyYIAuLi4rB792589dVXCAgIMGkfNmwYnJ2dTY57QUEBCgsLedxbYfz48Th79izOnDkjPsLCwjBr1izx7zzOD2706NGNli65cOEC+vbtCwAICAiAWq02Oc46nQ7Z2dk8zq1QWVkJBwfTjzFHR0cYDAYAPM6W0pLjGhERgdLSUuTk5Ih9vvrqKxgMBoSHh1u9ZslJPUO/I0pPTxcUCoXw/vvvC3l5ecKiRYsEDw8PQaPRSF1ah/Xcc88JSqVSOHLkiFBUVCQ+KisrxT5/+tOfBD8/P+Grr74STp06JURERAgRERESVm0f7r4aURB4nNvDiRMnBCcnJ2Ht2rXCxYsXhY8//ljo0qWL8NFHH4l91q1bJ3h4eAj//Oc/he+//1548sknhYCAAKGqqkrCyjuWmJgYoVevXsK+ffuES5cuCZ999png5eUlvPDCC2IfHue2KS8vF06fPi2cPn1aACBs2LBBOH36tHDlyhVBEFp2XCdMmCAMGTJEyM7OFo4dOyYEBgYKM2fOlOotSYphq402b94s+Pn5CXK5XBgxYoSQlZUldUkdGgCzj507d4p9qqqqhD//+c+Cp6en0KVLF+Gpp54SioqKpCvaTtwbtnic28fnn38uDBgwQFAoFEJQUJCwbds2k3aDwSCsXLlSUKlUgkKhEMaPHy8UFBRIVG3HpNPphCVLlgh+fn6Ci4uL8NBDDwmvvPKKoNfrxT48zm3z9ddfm/0/OSYmRhCElh3XmzdvCjNnzhS6du0quLu7C3PnzhXKy8sleDfSkwnCXUvtEhEREVG74pwtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyIIYtIiIiIgti2CIiIiKyoP8PKe1BZAsrdWUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100 # 베르누이 시행의 수\n",
    "p = 0.3 # 결과가 1일 확률\n",
    "X = binom.rvs(n, p, size=500, random_state=123)\n",
    "print(\"표본의 평균:\", np.mean(X), \"모집단(이론적) 평균:\", n * p)\n",
    "print(\"표본의 분산:\", np.var(X, ddof=1), \"모집단(이론적) 분산:\", n * p * (1 - p))\n",
    "sns.histplot(X)\n",
    "sns.scatterplot(\n",
    "    x=np.arange(0, 101), \n",
    "    y=binom.pmf(np.arange(0, 101), n, p), \n",
    "    ax=plt.gca().twinx(), color='orange', label='Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "584e30d5",
   "metadata": {},
   "source": [
    "**[Ex.2]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "1. X는 n = 100, p = 0.3인 이항분포를 따릅니다. $P(X=20)$을 구합니다.\n",
    "\n",
    "    \n",
    "2. X는 n = 100, p = 0.3 인 이항분포를 따릅니다. $P(X <= 20)$를 구합니다.\n",
    "\n",
    "    \n",
    "3. X는 n = 100, p = 0.3 인 이항분포를 따릅니다. $P(X <= A)=0.1$를 구합니다. 이 때, A를 구합니다.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4140da1d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. 0.007575644925726051\n"
     ]
    }
   ],
   "source": [
    "print(\"1. {}\".format(binom.pmf(20, n=100, p=0.3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2cba72e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. 0.016462853241869434\n"
     ]
    }
   ],
   "source": [
    "print(\"2. {}\".format(binom.cdf(20, n=100, p=0.3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f1a22432",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. 24.0\n"
     ]
    }
   ],
   "source": [
    "print(\"3. {}\".format(binom.ppf(0.1, n=100, p=0.3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04a72fb2",
   "metadata": {},
   "source": [
    "**[Ex.3]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$\\lambda$가 10인 포아송 분포에서 서로 독립인 표본 500개를 만들어 봅니다.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "733a3968",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "표본의 평균: 10.014 모집단(이론적) 평균: 10\n",
      "표본의 분산: 9.152108216432866 모집단(이론적) 분산: 10\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lamb = 10\n",
    "X = poisson.rvs(lamb, size=500, random_state=123)\n",
    "print(\"표본의 평균:\", np.mean(X), \"모집단(이론적) 평균:\", lamb)\n",
    "print(\"표본의 분산:\", np.var(X, ddof=1), \"모집단(이론적) 분산:\", lamb)\n",
    "sns.histplot(X)\n",
    "sns.scatterplot(x=np.arange(0, 31), y=poisson.pmf(np.arange(0, 31), 10), ax=plt.gca().twinx(), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e200794a",
   "metadata": {},
   "source": [
    "**[Ex.4]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "손님이 10분 동안에 평균 5명 온다고 할 때, 새로운 손님이 4분 이내에 올 확률을 지수 분포를 이용하여 구해봅니다. \n",
    "    \n",
    "손님이 오는 사건은 서로 독립입니다.\n",
    "    \n",
    "</div>\n",
    "\n",
    "**[풀이]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$\\lambda=5$, 4분의 확률변수 X = 4분 / 10분, \n",
    "\n",
    "$P(X \\le 0.4; \\lambda=5)$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0781a7cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8646647167633873"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 풀이 과정의 내용을 계산해봅니다.\n",
    "\n",
    "expon.cdf(0.4, scale=1/5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebf9aa06",
   "metadata": {},
   "source": [
    "## 3. 주요 분포의 특징"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "080d7450",
   "metadata": {},
   "source": [
    "### 정규분포\n",
    "\n",
    "**표준정규분포**: 평균이 0, 분산이 1인 정규 분포\n",
    "\n",
    "**중심극한정리**: 표본평균의 분포는 모집단의 분포와 상관 없이 표본의 크기가 커질 수록 정규 분포에 가까워진다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a2ef890",
   "metadata": {},
   "source": [
    "**[Ex.5]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$\\lambda$ 가 5인 포아송 분포에서 확률 변수를 n개씩 1000번 뽑아 각 표집의 표본평균을 구합니다.\n",
    "\n",
    "n을 5, 10, 30, 100 바꾸어 가며, Kolmogorov-Smironof로 정규성 검정을 하여 pvalue를 구합니다. \n",
    "\n",
    "(pvalue는 0과 1사이의 수이며 높을 수록 정규분포일 확률이 높음을 뜻합니다.)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f7b066df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "from scipy.stats import kstest\n",
    "fig, axes = plt.subplots(2, 2, figsize=(12, 7))\n",
    "for i, ax in zip([3, 10, 30, 100], axes.ravel()):\n",
    "    sam_mean = list()\n",
    "    for _ in range(1000):\n",
    "        X = poisson.rvs(mu=5, size=i) # mu ← lambda\n",
    "        sam_mean.append(X.mean())\n",
    "    sns.histplot(sam_mean, ax=ax)\n",
    "    _, pvalue = kstest(sam_mean, norm.cdf, args=[np.mean(sam_mean), np.std(sam_mean)])\n",
    "    ax.set_title('sample size: {}, pvalue:{:.3f}'.format(i, pvalue))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd17afd0",
   "metadata": {},
   "source": [
    "표본의 크기가 커질 수록 pvalue가 높아 집니다. 이는 곧 정규분포에 가까워짐을 의미합니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e762c3fe",
   "metadata": {},
   "source": [
    "## 카이제곱분포\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$Z_1, ... Z_k$이 서로 독립이고 표준정규분포인 확률 함수 일 때,\n",
    "\n",
    "$Q=\\sum_{i=1}^{k}Z_i^2$\n",
    "\n",
    "$Q \\sim \\chi^2_k$\n",
    "\n",
    "#### 감마분포와의 관계\n",
    "    \n",
    "$\\chi^2_k = \\Gamma(\\frac{k}{2}, \\frac{1}{2})$\n",
    "    \n",
    "</div>\n",
    "\n",
    "### t 분포\n",
    "\n",
    "- t분포는 표준정규분포($Z$)와 $\\chi^2_{n-1}$과의 아래와 결합으로 구성된 분포입니다. (n은 표본수)\n",
    "\n",
    "\n",
    "- 태생적으로, t분포는 모집단이 정규분포를 따른다는 가정을 하고 있습니다.\n",
    "\n",
    "> $t=\\frac{\\bar{X} - \\mu}{\\frac{s}{\\sqrt{n}}}$, s는 표본표준편차. $s=\\frac{1}{n-1}\\sum_{i=1}^{n}\\left(x_i - \\bar{x} \\right)^2$\n",
    ">\n",
    "> $t_{n-1} = \\frac{Z}{\\sqrt{\\frac{\\chi^2_{n-1}}{n-1}}}$\n",
    ">\n",
    "> $t_{\\nu} = \\frac{Z}{\\sqrt{\\frac{\\chi^2_{\\nu}}{\\nu}}}, \\nu=n-1$\n",
    "\n",
    "\n",
    "**유도 과정**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$s^2=\\frac{1}{n-1}\\sum_{i=1}^{n}\\left(X_i - \\bar{X}\\right)^2$\n",
    "\n",
    "$(n-1)s^2=\\sum_{i=1}^{n}\\left(X_i -\\mu + \\mu - \\bar{X}\\right)^2$\n",
    "\n",
    "$(n-1)s^2=\\sum_{i=1}^{n}\\left(\\left(X_i -\\mu\\right)^2 + 2 \\left(X_i -\\mu \\right) \\left(\\mu - \\bar{X}\\right) + \\left(\\mu - \\bar{X}\\right)^2\\right)$\n",
    "\n",
    "> $\\sum_{i=1}^{n}2 \\left(X_i -\\mu \\right) \\left(\\mu - \\bar{X}\\right) = \\sum_{i=1}^{n}2 \\left(X_i \\mu - X_i \\bar{X} - \\mu^2 + \\mu\\bar{X}\\right)$\n",
    ">\n",
    "> $= 2n \\left(\\bar{X}\\mu - \\bar{X}^2 - \\mu^2 + \\mu\\bar{X}\\right)$\n",
    ">\n",
    "> $= -2n\\left(\\bar{X} - \\mu \\right)^2$\n",
    "\n",
    "$(n-1)s^2=\\sum_{i=1}^{n}\\left(X_i -\\mu\\right)^2 - 2n\\left(\\bar{X} - \\mu \\right)^2 + n \\left(\\mu - \\bar{X}\\right)^2$\n",
    "\n",
    "$     = \\sum_{i=1}^{n}\\left(X_i -\\mu\\right)^2- n\\left(\\bar{X} - \\mu \\right)^2$\n",
    "\n",
    "$(n-1)\\frac{s^2}{\\sigma^2}=\\sum_{i=1}^{n}\\left(\\frac{X_i -\\mu}{\\sigma}\\right)^2 - n\\left(\\frac{\\bar{X} - \\mu}{\\sigma}\\right)^2=\\sum_{i=1}^{n}\\left(\\frac{X_i -\\mu}{\\sigma}\\right)^2 - \\left(\\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}\\right)^2$\n",
    "\n",
    "> $\\sum_{i=1}^{n}\\left(\\frac{X_i -\\mu}{\\sigma}\\right)^2 \\sim \\chi^2_n, \\left(\\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}\\right)^2 \\sim \\chi^2_1$\n",
    ">\n",
    "> $chi^2_{n-1} = chi^2_n - chi^2_1$\n",
    "\n",
    "따라서, $(n-1)\\frac{s^2}{\\sigma^2} \\sim chi^2_{n-1}$\n",
    "\n",
    "\n",
    "$t=\\frac{\\bar{X} - \\mu}{\\frac{s}{\\sqrt{n}}}=\\frac{\\frac{\\bar{X} - \\mu}{\\sigma}}{\\frac{\\frac{s}{\\sigma}}{\\sqrt{n}}}$ \n",
    "\n",
    "$=\\frac{\\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}}{\\frac{s}{\\sigma}}$\n",
    "\n",
    "$=\\frac{Z}{\\sqrt{\\frac{(n-1)\\frac{s^2}{\\sigma^2}}{n-1}}} \\sim \\frac{Z}{\\sqrt{\\frac{\\chi^2_{n-1}}{n-1}}}$\n",
    "\n",
    "</div>\n",
    "\n",
    "### F 분포\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$ F(d_1, d_2) = \\frac{S_1/d_1}{S_2/d_2} $ \n",
    "\n",
    "$S_1 \\sim \\chi^2_{d_1}$\n",
    "\n",
    "$S_2 \\sim \\chi^2_{d_2}$\n",
    "    \n",
    "</div>\n",
    "\n",
    "즉, F 분포는 분자는 자유도가 $d_1$인 카이제곱분포, 분모는 자유도가 $d_2$인 카이제곱분포인 형태를 하고 있습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4b77d99",
   "metadata": {},
   "source": [
    "## 4. 신뢰 구간\n",
    "\n",
    "- 신뢰 구간: 모집단의 모수에 대한 추정값이 존재할 것으로 예상되는 범위 나타냅니다.\n",
    "\n",
    "> 표본에서 얻은 정보를 이용하여 모집단의 모수에 대한 가능한 값의 범위를 제시합니다.\n",
    "\n",
    "- 신뢰 수준: 모집단의 모수가 신뢰 구간 내에 있을 확률입니다.\n",
    "\n",
    "> 신뢰 구간을 95% 정한다면, 모수가 신뢰 구간에 있을 확률이 95%라는 것입니다.\n",
    "\n",
    "- 신뢰 구간의 형태\n",
    "\n",
    "> 점 추정치(Point Estimate) ± 주변 오차 범위(Margin of Error)\n",
    "\n",
    "- 표본평균을 통한 신뢰 구간의 추청\n",
    "\n",
    "> $P(-c \\le 통계량 \\le c) = \\text{신뢰 수준}$\n",
    ">\n",
    "> $P(통계량 < -c) = \\frac{\\alpha}{2}$, $\\alpha(\\text{유의 수준}) = 1 - \\text{신뢰 수준}$\n",
    ">\n",
    "> $-c = F^{-1}(\\alpha/2)$, $F^{-1}$는 통계량의 분포의 누적확률함수의 역함수(Percentile Point Function)\n",
    ">\n",
    "> $c = -F^{-1}(\\alpha/2)$\n",
    "\n",
    "\n",
    "1. 모분산을 알고 있을 경우\n",
    "\n",
    "> 정규분포를 사용합니다.\n",
    ">\n",
    "> $Z(\\text{통계량}) = \\frac{\\bar{X} - \\mu}{\\sigma/\\sqrt{n}}$\n",
    ">\n",
    "> $c = -Z_{\\alpha/2}$, $-Z_{\\alpha/2}$는 정규분포에서의 $F^{-1}(\\alpha/2)$ 입니다.\n",
    ">\n",
    "> $-Z_{\\alpha/2} \\le \\frac{\\bar{X} - \\mu}{\\sigma/\\sqrt{n}} \\le Z_{\\alpha/2}$\n",
    ">\n",
    "> $\\bar{X} -Z_{\\alpha/2}\\frac{\\sigma}{\\sqrt{n}} \\le \\mu \\le \\bar{X} + Z_{\\alpha/2}\\frac{\\sigma}{\\sqrt{n}}$\n",
    "\n",
    "2. 모분산을 모를 경우 \n",
    "\n",
    "> t-분포를 사용합니다. \n",
    ">\n",
    "> $t(\\text{통계량}) = \\frac{\\bar{X} - \\mu}{S/\\sqrt{n}}$\n",
    ">\n",
    "> $c = -t_{\\alpha/2,\\nu=n-1}$, $-t_{\\alpha/2,\\nu=n-1}$는 t분포에서의 $F^{-1}(\\alpha/2)$ 입니다.\n",
    ">\n",
    "> $-t_{\\alpha/2,\\nu=n-1} \\le \\frac{\\bar{X} - \\mu}{S/\\sqrt{n}} \\le t_{\\alpha/2,\\nu=n-1}$\n",
    ">\n",
    "> $\\bar{X} -t_{\\alpha/2,\\nu=n-1}\\frac{S}{\\sqrt{n}} \\le \\mu \\le \\bar{X} + t_{\\alpha/2,\\nu=n-1}\\frac{S}{\\sqrt{n}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d141e1f",
   "metadata": {},
   "source": [
    "**[Ex.6]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "    \n",
    "모분산이 4인 모집단에서 100개의 표본을 뽑았습니다. 이 때, 표본 평균이 124 입니다. \n",
    "\n",
    "표본수 100개는, 표본평균의 분포가 정규분포를 따르기에 충분한 수라고 가정합니다.\n",
    "\n",
    "이 때, 모평균의 신뢰구간을 구하세요.(신뢰수준이 95%)\n",
    "    \n",
    "</div>\n",
    "\n",
    "**[풀이]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$\\alpha = 1 - 0.95 = 0.05$\n",
    "    \n",
    "$124 - Z_{0.025}\\frac{2}{10} \\le \\mu \\le 124 + Z_{0.025}\\frac{2}{10}$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5e7e1413",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(123.60800720309199, 124.39199279690801)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 풀이 과정의 내용을 계산해봅니다.\n",
    "\n",
    "sigma2 = 4\n",
    "n_sample = 100\n",
    "x_bar_std = (sigma2 / n_sample) ** 0.5\n",
    "x_bar = 124\n",
    "c = -norm.ppf(0.025)\n",
    "x_bar - x_bar_std * c, x_bar + x_bar_std * c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7058f083",
   "metadata": {},
   "source": [
    "**[Ex.7]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "모집단은 정규분포를 따르고 25개 표본을 뽑았습니다. 이 때, 표본 평균이 104이고, 표본 분산이 9입니다.\n",
    "    \n",
    "모평균의 신뢰구간을 구하세요.(신뢰수준이 95%)\n",
    "\n",
    "</div>\n",
    "\n",
    "**[풀이]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "$104 -t_{0.025,\\nu=24}\\frac{3}{5} \\le \\mu \\le 104 + t_{0.025,\\nu=24}\\frac{3}{5}$\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "577f80ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(102.76166086302318, 105.23833913697682)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 풀이 과정의 내용을 계산해봅니다.\n",
    "\n",
    "s2 = 9\n",
    "n_sample = 25\n",
    "s_div_sq = (s2 / n_sample) ** 0.5\n",
    "x_bar = 104\n",
    "c = -t.ppf(0.025, df=n_sample-1)\n",
    "x_bar - s_div_sq * c, x_bar + s_div_sq * c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bdf939ca",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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