{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "eafab3fb-c893-4bed-ac24-5af9126750a8",
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"---------------------------------\n",
"Working on the host: Joachims-MacBook-Pro.local\n",
"\n",
"---------------------------------\n",
"Python version: 3.10.2 | packaged by conda-forge | (main, Feb 1 2022, 19:30:18) [Clang 11.1.0 ]\n",
"\n",
"---------------------------------\n",
"Python interpreter: /opt/miniconda3/envs/srh/bin/python\n"
]
}
],
"source": [
"%matplotlib inline\n",
"# Load the \"autoreload\" extension\n",
"%load_ext autoreload\n",
"# always reload modules\n",
"%autoreload 2\n",
"# black formatter for jupyter notebooks\n",
"#%load_ext nb_black\n",
"# black formatter for jupyter lab\n",
"%load_ext lab_black\n",
"\n",
"%run ../../src/notebook_env.py"
]
},
{
"cell_type": "markdown",
"id": "2bc6e545-48d5-49c6-b69c-5b15ed51821e",
"metadata": {},
"source": [
"# Die Student t-Verteilung"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b6976869-d39f-4cd3-9c62-e6a5feebac6b",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy.stats import t"
]
},
{
"cell_type": "markdown",
"id": "a847a2f6-9a85-4f23-9439-d6922d85ae42",
"metadata": {},
"source": [
"Die Studentsche $t$-Verteilung ist nach William Sealy Gosset ($1876-1937$) benannt, der sie $1908$ erstmals bestimmte. Gosset war einer der besten Oxford-Absolventen in Chemie und Mathematik seiner Generation. Im Jahr $1899$ nahm er eine Stelle als Brauer bei Arthur Guinness Son & Co, Ltd in Dublin, Irland, an. Bei seiner Arbeit für die Guinness-Brauerei interessierte er sich für die Qualitätskontrolle anhand kleiner Proben in verschiedenen Stadien des Produktionsprozesses. Da Guinness seinen Angestellten die Veröffentlichung von Papieren untersagte, um die Weitergabe vertraulicher Informationen zu verhindern, hatte Gosset seine Arbeit unter dem Pseudonym \"Student\" veröffentlicht, und seine Identität war einige Zeit nach der Veröffentlichung seiner berühmtesten Errungenschaften nicht bekannt, so dass die Verteilung den Namen \"Studentsche\" oder \"$t$-Distribution\" erhielt, wodurch sein Name weniger bekannt wurde als seine wichtigen Ergebnisse in der Statistik ({cite:p}`Dümbgen2016` s.81)."
]
},
{
"cell_type": "markdown",
"id": "dcf570e4-2841-4316-b49c-45cbc19b4f48",
"metadata": {},
"source": [
"Die $t$-Verteilungskurve ist, wie die Normalverteilungskurve, symmetrisch (glockenförmig) um den Mittelwert. Die $t$-Verteilungskurve ist jedoch flacher als die Standard-Normalverteilungskurve. Folglich hat die $t$-Verteilungskurve eine geringere Höhe und eine breitere Streuung als die Standardnormalverteilung."
]
},
{
"cell_type": "markdown",
"id": "c6ef251b-457c-4a61-94b6-f3863495fe61",
"metadata": {},
"source": [
"Die $t$-Verteilung hat nur einen Parameter, die sogenannten **Freiheitsgrade** ($df$). Die Form einer bestimmten $t$-Verteilungskurve hängt von der Anzahl der Freiheitsgrade ($df$) ab. Die Anzahl der Freiheitsgrade für eine $t$-Verteilung ist gleich dem Stichprobenumfang minus eins, das heißt,"
]
},
{
"cell_type": "markdown",
"id": "143c906d-483c-49eb-ab35-f1971eba018b",
"metadata": {},
"source": [
"$$df = n - 1$$"
]
},
{
"cell_type": "markdown",
"id": "f1d123e1-801d-45b2-9752-7b472b790286",
"metadata": {},
"source": [
"Wenn der Stichprobenumfang $n$ und damit $df$ zunimmt, nähert sich die $t$-Verteilung der Standardnormalverteilung an. Die Einheiten einer $t$-Verteilung werden mit $t$ bezeichnet. Der Mittelwert der $t$-Verteilung ist gleich $0$, und ihre Standardabweichung beträgt $ \\sqrt{df/(df-2)}$ ({cite:p}`fahrmeirstatistik` s.280,s.284)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "bc599b9e-2375-4e25-be49-382e0ce705a8",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import t, norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"df = [1, 3, 8, 30]\n",
"\n",
"x = np.linspace(-4, 4, 1000)\n",
"fig, ax = plt.subplots()\n",
"for _df in df:\n",
" ax.plot(x, t.pdf(x, df=_df), label=f\"df={_df}\")\n",
"ax.plot(x, norm.pdf(x), label=f\"normal\", color=\"k\", linestyle=\"dashed\")\n",
"ax.vlines(x=0, ymin=0, ymax=norm.pdf(0, 0, 1), color=\"k\")\n",
"ax.set_yticks([])\n",
"ax.set_title(\n",
" \"Vergleich der t-Warscheinlichkeitsdichtefunktion\\nmit unterschiedlichen Freiheitsgraden (df) und\\nder Warscheinlichkeitsdichtefunktion der Normalverteilung\"\n",
")\n",
"ax.legend(fontsize=18)"
]
},
{
"cell_type": "markdown",
"id": "59ca300b-c7b0-49ee-a440-feb8acefe0ec",
"metadata": {},
"source": [
"### Grundlegende Eigenschaften von t-Kurven"
]
},
{
"cell_type": "markdown",
"id": "1232ff63-9c38-4501-a3c3-94b2a61d265a",
"metadata": {},
"source": [
"\n",
" - Die Gesamtfläche unter einer $t$-Kurve ist gleich $1$.\n",
" - Eine $t$-Kurve erstreckt sich unendlich in beide Richtungen und nähert sich dabei der horizontalen Achse, berührt sie aber nie.\n",
"- Eine $t$-Kurve ist symmetrisch um $0$.\n",
"- Mit zunehmender Anzahl von Freiheitsgraden ähneln $t$-Kurven immer mehr der Standard-Normalverteilung."
]
},
{
"cell_type": "markdown",
"id": "9a79a626-9f31-463c-a8b0-2dd0293ac168",
"metadata": {},
"source": [
"## Die Studentsche-t-Verteilung in Python\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "6510d05d-525c-4045-959a-018a5052902e",
"metadata": {},
"source": [
"Python ermöglicht den Zugriff auf die $t$-Verteilung mit den Funktionen `t.pdf()`, `t.cdf()`, `t.ppf()` und `t.rvs()`. Wenden Sie die Funktion `dir()` auf diese Funktionen an, um weitere Informationen zu erhalten.\n",
"\n",
"Die Funktion `t.rvs()` erzeugt Zufallsabweichungen der $t$-Verteilung und wird als`t.rvs(df, loc , scale, size)` geschrieben. Wir können leicht eine Anzahl von $n$ Zufallsstichproben erzeugen. Erinnern Sie sich daran, dass die Anzahl der Freiheitsgrade für eine $t$-Verteilung gleich dem Stichprobenumfang minus eins ist, d.h.,\n"
]
},
{
"cell_type": "markdown",
"id": "39f5660a-e46c-445b-bfdf-27620dfacfa1",
"metadata": {},
"source": [
"$$df = n - 1\\text{.}$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "f7e67286-1e9c-4508-a039-588a6a4ca38c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.57219722, -1.06637478, -0.71077868, 1.65785187, 0.00215566,\n",
" 0.45627384, -1.03298084, 0.72441145, -0.23646133, -0.58847821,\n",
" 0.21009352, -1.88866804, 0.58356278, 0.70377475, 1.23205156,\n",
" 1.43597651, -1.00714028, 1.10367847, 0.4193459 , 0.25581504,\n",
" -0.55267188, -0.54728603, -0.04414093, -0.43147301, 1.01897465,\n",
" -1.08946951, 0.05216556, 0.51312979, 0.3854111 , -0.17321186])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Generiere Zufallswerte der t Verteilung mit df = 29 und Stichprobengrösse = 30\n",
"n = 30\n",
"t.rvs(df=n - 1, size=n)"
]
},
{
"cell_type": "markdown",
"id": "be8d8a32-5996-43f5-94f6-0f7aa746cf05",
"metadata": {},
"source": [
"Außerdem können wir eine sehr große Anzahl von Stichproben erzeugen und sie als Histogramm darstellen.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "34d482b7-a5e3-4a2f-a73e-936cd4fd1ed7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Generiere Zufallswerte der t Verteilung mit df = 9999 und Stichprobengrösse = 10000\n",
"n = 10000\n",
"y = t.rvs(df=n - 1, size=n)\n",
"fig, ax = plt.subplots()\n",
"ax.set_title(\"Histogramm der Stichproben\")\n",
"_ = ax.hist(y, bins=40, density=True, edgecolor=\"k\")"
]
},
{
"cell_type": "markdown",
"id": "4e4e849e-c474-412e-84a3-2fec054828b8",
"metadata": {},
"source": [
"Mit der Funktion `t.pdf()` können wir die Wahrscheinlichkeitsdichtefunktion und damit den vertikalen Abstand zwischen der horizontalen Achse und der $t$-Kurve an jedem beliebigen Punkt berechnen. Zur Demonstration konstruieren wir eine $t$-Verteilung mit $df=5$ und berechnen die Wahrscheinlichkeitsdichtefunktion bei $t=-4,-2,0,2,4$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "15cc1195-cf6d-442b-88c7-0894a4702967",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.00512373, 0.06509031, 0.37960669, 0.06509031, 0.00512373])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = [-4, -2, 0, 2, 4]\n",
"y_t = t.pdf(x, df=5)\n",
"y_t"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "6d4afea8-1632-4f57-9753-f2acb1171dd6",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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apKdw+yk9w44TMz8b2J5DuzXnr+/OZdnGnWHHERGJiaouyrdGnkt2K6lHUJCXOUWcu29290/c/d/A6QRdYc6MrPvO3b8sscu4yHPffU4tIhKH/jV+AXPXbOfuM3vTqG5K2HFixsz46xm9SUowbvjPNHVjEZEaqaqL8qIbMTNKLM8A5nkpQ8GY2WlmNqjE4plAHtDWzJLM7GIzO6DENkUdKzVWuYjUOHPXbGP0xEWcNaAdR+zXMuw4MdemUR1ujnRjeUHdWESkBgqjKF8OnFa0IDIk4onA+DL2uRG4p8Syw4FkYIa75wO3A7eV2OZMgsJ98r6GFhGJJ4WFzk2vz6BBnWT+eEKPKj9//46N6d+xcZWf92cD2zOsazP+Nm4ea7dVTZ92EZGqUqVFeaQl/G7gCjO7y8xOAN4EmgH3A5hZppkNLrbbXcBwMxttZkea2ZXAy8AE4N1i25xiZg+Y2VFmdhNBIf8vd1eTiojUKP/+ZhnfLdvCzSf2oHF61Xdb+cNx+/GH4/ar8vOaGXee2ovcgkLufEeTColIzVLlg9m6+yPA9cAI4DWgEXCsuy+KbHILxVq33f1tgpk8+wNvR9Y/B5xY1N3F3ccAlxC0oL8NjATuBG6I/XckIlJ11m3P4e735jI0symnH9A27DhVrlOzdH51WBfemb6aT+dr9CwRqTmqdEbPeKQZPUWkOvnNv79j3Mw1jLtmGBnN64WS4YrnpgIwasSAUM6/O7+A4/75Ge7OuGuGk5b8kykuRETiUjzN6CkiInvpswXreWvaKq46PDO0ghxg885cNu/MDe38qUmJ3HlqL5Zs3MmjE7JCyyEiUplUlIuIVAN5BYXc9tYsOjWty5WHZYYdJ3SHdG3GKX3b8OiELBZvKHM0XRGRakNFuYhINfDc5KVkrc/m5hP3JzVJ3TUAbj6xB8mJxl1j54QdRURkn6koFxGJcxt37Ob+j+YzrGszjuzRIuw4caNFgzR+dUQXPpqzls8XaEoKEaneVJSLiMS5+z6cz87cAm49aX/MLOw4HNylGQd3aRZ2DAAuPbgz7ZvU4c53ZpNfUBh2HBGRvaaiXEQkjs1etY1/f72MEYM70rVl/bDjAPCbI7vymyO7hh0DgLTkRP7v+B7MW7udl75ZHnYcEZG9pqJcRCROuTt3vDOLhnWSufaobmHHiVvH9WrFgZ2bcN+H89m6Ky/sOCIie0VFuYhInPpozjq+XLSJ647uRsO6yWHH+cFFT37NRU9+HXaMH5gZt560P5t35vLQxwvCjiMisldUlIuIxKH8gkL+Pm4uGc3SOffADmHH+ZGcvAJy8grCjvEjvdo25GcD2vP0F0tYtnFn2HFERCpMRbmISBz6z7crWLBuBzcc153kRP2ojsa1R3cjwYz7PpwXdhQRkQrTT3oRkTizK7eA+z9cwAEdGnFsz1Zhx6k2WjVM49JDOvPmtFXMWrU17DgiIhWiolxEJM489cVi1mzL4cbj9ouLIRCrkysOzaRBWjJ/H6fWchGpXlSUi4jEkc3ZuTw6IYsj92vBQRlNw45TqiN7tIjbSYwa1knmqsMymTh/PV9kaUIhEak+VJSLiMSRhz9ZSPbufG44br+wo5Rp5PBMRg7PDDtGmS4a2onWDdP427h5uHvYcUREoqKiXEQkTqzYvJNnJy/lzP7t6N4qPiYKqo7SkhO59qhuTFu+hXEz14QdR0QkKirKRUTixIPjF4IFo4jEs3NGT+ac0ZPDjlGuM/q3pUuLevzj/XnkFxSGHUdEZI9UlIuIxIElG7J57dsVnH9gB9o0qhN2nGovKTGB64/tzqIN2fzn2xVhxxER2SMV5SIiceBf4xeQnGhcdXj89tWubo7ZvyW92zbkwY8Xkpuv1nIRiW8qykVEQrZw3Q7e+H4lIwZ3pEX9tLDj1BhmxnVHd2PF5l1qLReRuKeiXEQkZA+MX0BaciJXHKpW8sp2WPfm9GvfiIfUWi4icU5FuYhIiOat2c4701dx0dBONK2XGnacqJzUpzUn9WkddoyomBnXHt2NlVt28cqU5WHHEREpU1LYAUREarN/fjSf9JQkRg7LCDtK1EYM6RR2hAoZ3rUZAzo25uFPFnLWgHakJSeGHUlE5CfUUi4iEpJZq7by3sw1XHpIZxqnp4QdJ2q7cgvYlVsQdoyoFfUtX701h5e/UWu5iMSnUIpyM7vMzBaY2S4zm2xmQ/aw/bFm9o2ZZUf2u9rMrMQ2w8zsKzPbGdnm0th+FyIi++b+DxfQIC2JXxzSOewoFXLxU19z8VNfhx2jQoZmNuXAzk14ZMJCcvKqzx8UIlJ7VHlRbmYXAqOA54EzgS3A+2ZW6m+lSMH+DjATOBV4DLgPuKbYNj2AccBi4AzgbeAJMzsrVt+HiMi+mLFiKx/NWctlwzJoWCc57Dg1nplx7VHdWLttNy9+tSzsOCIiP1GlRXmkdfsOYIy73+7u7wKnABuAa8vY7VpgFnCpu3/k7n8nKOh/VWybG4ElwHnuPs7dr4tsc2tsvhMRkX3z4MdBK/nFB3cKO0qtMSSzKUMymvLIhKxq1f1GRGqHqm4p7wJ0BN4qWuDuecBY4Lgy9vkdQbHtxZblAsWHKTgKeKfENm8Avc2sTSXkFhGpNHPXbOOD2Wu55ODO1E9TK3lVuuaormzYsZuXv1FruYjEl6ouyrtFnheWWL4IyDSzn9wS7+7L3X0OgJk1inR/KeoCg5mlA23KOGbxc4qIxIWHP8kiPSWRS9RKXuUOymjKgZ2aMPrTRezOV2u5iMSPqi7KG0Set5dYvj2SJb2sHc2sI7AZeIagf/mjURyz+HoRkdBlrd/BO9NXMWJIJxrVrT4jrhR31oB2nDWgXdgx9tqvj+jC6q05vP7tyrCjiIj8oKqL8qIRU7yM5eVNt7YNOAI4H2gMTDazuntzTDMbaWZTzGzK+vXro80uIrLPHvkki9SkBH45rHqNuFLc2QPbc/bA9mHH2GvDujajb7uGPDJhIfkFmuVTROJD1EW5mSWZ2QVm9pSZvWdmXc3sEjPrU4HzbY081y+xvB5B8Zxd1o7uvtndP3H3fwOnE3RLOZOgWC/rmMXPWfxYY9x9oLsPbN68eQXii4jsveWbdvLG9ys5/8CONKsms3eWZlN2Lpuyc8OOsdfMjF8f0ZXlm3bx1rRVYccREQGiLMrNrCnwJfAU0B84hqAIPgP4wswOivJ8CyLPJaeuywDmlbhRs+jcp5nZoBKLZwJ5QFt33wGsLuOYAPOjzCYiElOPTswi0YyRw6vP7J2lufL5qVz5/NSwY+yTI/drwX6t6vPwJwspLPzJrx4RkSoXbUv5/UBDgtFTBvC/riFnAV8Bf4nyOAuA5cBpRQvMLBk4ERhfxj43AveUWHY4kAzMiLweD5xc4kbR04CZ7r42ymwiIjGzeusuXpuygrMHtqNVw7Sw49R6CQnGr4/oQtb6bMbNWhN2HBGRqIvyk4E/uvtSivXddvfdwL0EhfoeRVrC7wauMLO7zOwE4E2gGUHhj5llmtngYrvdBQw3s9FmdqSZXQm8DEwA3o1scw/QHXjVzI43s3uBCwjGRBcRCd2YTxdR4M4Vh2aGHUUiju/Vmozm6Tz48UJK+aBWRKRKRVuUJwI5ZaxL4n8t53vk7o8A1wMjgNeARsCx7l40hOEtwORi279NMJNnf4KZOm8BngNOLOru4u7TCP5wyAD+G/n6End/NdpcIiKxsn77bv799TJOP6At7ZvUDTuORCQmGFcd1oU5q7fx8dx1YccRkVou2qL8Y+BPZta42DKPdD35LTCxIid193vdvYO713X3oe5evAi/2N2txPZvufugyPZt3P06d99ZYpv33b2fu6e5ezd3f7oimUREYuWJzxezO7+Qqw5TK3m8ObVfG9o1rqPWchEJXbRF+e+AtkAWwWycDtwJzAH6AjfEJJ2ISDW3OTuX5yYv4aQ+bchoXm/PO1QDFwzuyAWDO4Ydo1IkJyZw5WGZfL98C5MWbgw7jojUYlEV5e6eBfQBRgNNCIrzlgTdSQ5w97kxSygiUo09M3kJ2bkF/OrwmtNKfnLfNpzct03YMSrNWQPa0bJBKg9/UnJiaBGRqhPtkIgdgM3ufpO7D4l0Dxnk7tcC60vcmCkiIsDO3Hye+WJJZPi9mjO58Kotu1i1ZVfYMSpNalIivzwkg8mLNjJt+Zaw44hILRVt95XFQL8y1h1E0OdcRESKeeWb5WzemccVNawv+bUvf8+1L38fdoxKdd5BHWiQlsSoiVlhRxGRWiqprBVmNgoo+nzSgHvNbEspm/YANlR+NBGR6iuvoJDHPlvMgI6NGdSpSdhxZA/qpSYxYkhHHpmQRdb6HWTWkP7/IlJ9lNdS/i7BrJ1F09enF3td9KgLTAPOjWFGEZFqZ+z01azcskvjklcjFw/tTEpiAo99umjPG4uIVLIyW8rd/S2CkVYws0+Aq9x9TlUFExGprtydUROz6NqiHkfu1yLsOBKl5vVTOXtgO175ZgXXHt2Nlg0086qIVJ1oR185XAW5iEh0Jsxfz9w12xk5PIOEhKjnVpM4MHJYJvmFhTz5+eKwo4hILVNmS3lxZpYO3AYcTjAD50+KeXfPqMxgIiLV1agJWbRumMap/dqGHSUmLhtWc3/cd2halxP7tOGFr5Zx1eFdaFgnOexIIlJLRFWUAw8DPyfoZz4JKIxZIhGRauy7ZZv5avEmbj6xBylJ0Q5wVb0ctX/LsCPE1BWHZvD2tFU8/+VSfnV4l7DjiEgtEW1Rfhrwe3d/IIZZRESqvVETs2iQlsS5B3YIO0rMZK3fAVBjRyjp2aYhw7s156lJi/nFIZ1JS04MO5KI1ALRNuMUADNiGUREpLrLWr+DD2av5cIhnaiXGm2bR/Xzf6/P4P9er9m/Eq48NJMNO3J5beqKsKOISC0RbVH+EvDLWAYREanuxkxcREpiAhcf3CnsKLKPBmc0oW/7Roz5dBH5BeqxKSKxV97kQf8q9jIFONvM+gBfAjtLbO7u/tsY5BMRqRbWbsvhv9+t5JxB7WlWLzXsOLKPzIwrD83kiuen8t7MNZzct82edxIR2Qflfb56conXKwgmEDqylG0dUFEuIrXWk58vJr+wsEaPTFLbHLN/SzKap/PohCxO6tMaMw1vKSKxU97kQZ2rMoiISHW1dVceL3y1jBP7tKFD07phx5FKkpBgXDE8kxv+M53PFmxgeLfmYUcSkRos6vG6zOwcM3uw2OshZva5mZ0Um2giItXDC18tZcfufC4fXjtaya8+oitXH9E17BhV4tQD2tCyQSqjJmaFHUVEarioinIz+yXwb4KJg4psAFYCb5jZmZUfTUQk/uXkFfDk50sY1rUZvdo2DDtOlTikazMO6dos7BhVIjUpkV8eksEXWRv5fvmWsOOISA0WbUv574A73X1E0QJ3X+Du5wB/AW6NRTgRkXj3+rcr2bBjN1cemhl2lCoza9VWZq3aGnaMKnPeQR1okJbEaLWWi0gMRVuUdwQmlrFuIlA7PscUESmmoNAZ82kWfdo1ZEhm07DjVJk73p7NHW/PDjtGlamXmsSIIR0ZN2sNiyITJ4mIVLZoi/JFwHFlrDsSWF45cUREqo/3Z61hycadXHFopkbmqOEuHtqZ5MQEHvtsUdhRRKSGinbKuX8Bj5pZI+AdYB3QHDgJuBS4OibpRETilLszamIWnZulc2zPVmHHkRhrXj+Vswe049UpK7j2qG60aJAWdiQRqWGiail39zHA9cDpwBvAJOBN4EzgD+4+KlYBRUTi0eSsjUxfsZXLhmWQmKBW8tpg5PAM8gsLeXLSkrCjiEgNFPWQiO5+H9AC2B8YBvQGWkaWi4jUKo9OzKJZvVTO6N827ChSRTo2Tef43q154culbMvJCzuOiNQwZRblZtbEzBKKfd0EaEzQdWUusBpoWGxd1MzsMjNbYGa7zGyymQ3Zw/ZDzewTM9tiZqvM7Fkza1lim5lm5iUeGyqSS0QkGjNXbuWzBRu49JBOpCUnhh2nyt1wXHduOK572DFCccXwTLbvzufFr5aFHUVEapjyWsrXAwMjX2+IvC7vERUzuxAYBTxP0P1lC/C+mZU6g6iZ9QDGA9uB84DfAwdH9kmObJMCdANuBIYUexwbbS4RkWiN/nQR9VKT+PlBHcOOEooBHZswoGOF2mJqjN7tGnJwl6Y8+fliducXhB1HRGqQ8m70vBTIKva17+vJLBie4A5gjLvfHln2ITAPuBb4TSm7/ZqgVf5Md8+L7LMA+Bo4GniXoEtNMvCmu8/d15wiImVZvmknY6ev4rJhGTSskxx2nFBMXboJoNYW5lccmsmIJ77mje9Wcs6gDmHHEZEaosyi3N2fKfb105V0vi4EY56/VezYeWY2lrKHXJwFzC4qyCPmRZ6LWtf7ADnAgkrKKSJSqsc+W0RignHJwaV+uFcr/H1c8CP45cvL7XlYYx3SpRk92zRg9KeLOHtAexJ0o6+IVIIyi3Izu64iB4ryhs9ukeeFJZYvAjLNLNHdf/R5oLs/UspxTo48F7WK9wE2Ai+b2TEErfqvAte6+/Zo8ouI7MnGHbt5ZcpyTj+gLa0aaki82srMuOLQTK7+93d8MHstx/XSkJgisu/K675yT4nXDhhQQNCHvDGQCuQCm4BoivIGkeeShfJ2gv7t6cC28g5gZu0j2aYAH0cW9wFaAdOAB4B+BN1kOhNMblTyGCOBkQAdOuijRxGJzjOTl5KTV8jI4RlhR5GQHd+rFR2a1GXUxCyO7dlSk0eJyD4r80ZPd08oehB0LVlHcGNmqru3cfc6wDHAWuCGKM9X9FOrZP/0ouWF5e4cFOTjI7nPdfei4/wBOMTd73T3z9z9QeAK4AgzG1bK9zbG3Qe6+8DmzZtHGV1EarOdufk8O3kJR+/fki4t6ocdR0KWlJjAZcMz+H75Fr5avCnsOCJSA0Q7TvlDwP+5+3/d/YfC2d0/Av4I3BXlcbZGnkv+RqtHUJBnl7WjmfUCviBobT/a3YtuQsXdv3P3L0vsMi7y3DfKbCIiZXr5m+Vs2ZnHFYeqlVwCZw9oR9P0FEZNzNrzxiIiexBtUd6asoc93Ak0ivI4RTdilvytlgHMK9by/SNmdhDwKUHXmWHuPr3YuiQzu9jMDiixW53Is8YqF5F9kldQyOOfLWZQp8a1dsSR4m49eX9uPXn/sGOELi05kYuHdmLCvPXMWV1uz0sRkT2KtiifBNxuZm2KLzSzTODPwEdRHmcBsBw4rdgxkoETCbql/ISZdQLeI+gmM9TdfzTCirvnA7cDt5XY9UwgD5gcZTYRkVKNnb6alVt2cfnwzLCjxIWebRrSs03DsGPEhRFDOlI3JZHRai0XkX0UbVF+NUFr+WIzm2Jm48zsW2AOkBhZv0eRlvC7gSvM7C4zOwF4E2gG3A9BoW9mg4vt9gBBl5U7gA5mNrjYo3Vkm7uAU8zsATM7ysxuIrgZ9F/uvjTK71FE5CfcnVETs+jaoh5H7Nci7Dhx4fMFG/h8gT6EBGhUN4XzDuzA29NXs3zTzrDjiEg1FlVRHmmd7g5cTzCcoREMR/groI+7r4r2hJEhDq8HRgCvEXR9OdbdF0U2uYVI63akFf0EgsL/xcjy4o+fR445BrgEOBx4m2BklTuJ/gZUEZFSTZy/nrlrtjNyeIbGo4548OMFPPixpoUo8otDOmPAE58vDjuKiFRj5Q2J+COR8b7/FXlgZklAQ3ffXdGTuvu9wL1lrLsYuDjydR7BTJ3RHPNp4OmKZhERKc/oiYto1SCNU/u1DTuKxKk2jepwar+2vPzNcn57ZFcap6eEHUlEqqGoWsrNLDXS3eSCyOshBEMkrjOzCWbWLJYhRUTCMG35FiYv2sgvDulMSlK0vf2kNrri0Ax25RXwzOQlYUcRkWoq2t8yfwWu5X+t1s8BKwi6jLTipxMNiYhUe6M/zaJ+WhLnHtg+7CgS57q2rM9RPVrwzBdL2JmbH3YcEamGoi3KzyaYsv4pMxtEMIThn939WeBmgtFTRERqjMUbsnlv5hpGDO5I/bSoetFJLXfFoZls3pnHK98sDzuKiFRD0fYpbwbMjnx9EsFQg+9FXm8C0io5l4hIqB77bBHJiQlcfHCnsKPEnb+c0TvsCHFpYKcmDOzYmMc+W8zPB3ckOVFdnkQketH+xMgCDo6MhvIz4PPIjZ8A5wLzYxFORCQM67bn8NrUFZzZvx0t6qvNoaTM5vXIbF4v7Bhx6fJDM1m5ZRdjp68OO4qIVDPRFuX/IJgkaD3QDbgPwMwmA5cSjD0uIlIjPPPFEvIKCrlsWOewo8Slj2av5aPZa8OOEZeO3K8FXVvUY9TELMqYpFpEpFTRjlP+DHAIQWE+3N3HRlaNA45w91djlE9EpErt2J3Pc5OXclzPVmSoNbhUj322iMc+W7TnDWuhhARj5PAM5q7ZzoT568OOIyLVSLRDIl4ILHD3e9x9UtFyd78dmG9mv49VQBGRqvTS18vYlpPP5Ydmhh1FqqlT+7WldcM0Rk/MCjuKiFQj0XZfeYpgxJXSHEjQgi4iUq3l5hfy+GeLGZzRhH7tG4UdR6qplKQEfnFIZ75ctInvl28JO46IVBNlFuVmNt7MtpnZNsCAT4peF38ArwPTqiqwiEisvDVtFWu25aiVXPbZuQd2oEFaEqMmqLVcRKJT3pCIVxOMT27ArcC/CSYMKq4A2AK8FItwIiJVpbDQGTUxi/1a1eewbs3DjiPVXL3UJC4c0omHJywka/0OjVYjIntUZlHu7rOB2wHMzIHH3H1VVQUTEalKH8xey8J1O3jg3H6YWdhx4tr95/QLO0K1cPHBnRjz2SIe+3QRd5/ZJ+w4IhLnyizKzaw/MMfddwFvA63MrFVZ27v7tzHIJyISc+7OIxMW0rFpXU7s3TrsOHGvTaM6YUeoFprVS+XsAe14dcoKrju6Gy0aaMx7ESlbeTd6TgF6F/v6mzIeRetERKqlSQs3Mn3FVq44NJMkzcK4R29PW8Xb0/TBaTRGDs8gv7CQJyYtDjuKiMS58vqUHw7MLva1iEiN9PAnC2nZIJUz+rcNO0q18PyXSwE4uW+bkJPEv45N0zm+d2te/HIZvzq8Cw3SksOOJCJxqrw+5RNL+9rMkoBmwAZ3z49tPBGR2Jq6dDOTF23k5hN7kJqUGHYcqYGuPDSTsdNX88KXy7jyMI3sIyKli/pzWjMbbGYfATsIRmHpY2bPm5nGKBeRauvRCQtpVDeZ8w7sEHYUqaF6tW3IIV2a8eSkxeTkFYQdR0TiVLQzeh4BFLWW/5FgmESAmcCNZnZdDLKJiMTU3DXb+GjOOi4Z2pn01PJ684nsmysOzWT99t3897uVYUcRkTgVbUv534CX3f0o4AEiRbm73w3cBYyMTTwRkdh5dEIW6SmJXDS0Y9hRpIY7uEtTerdtyKiJWeQXFIYdR0TiULRFeS/g+cjXXmLdJ4B+o4lItbJ0YzZvT1vFBYM70qhuSthxqpVHLxjAoxcMCDtGtWJm/PqILizduJN3pq8OO46IxKFoi/J1wP5lrOsRWS8iUm2MmriIpMQEfnFI57CjVDtN0lNokq4/ZCrq6B4t6d6yPg99spDCwpLtWyJS20VblD8D3GlmlwBF808nmdlRwG3AizHIJiISE2u35fCfqSs4e0A7TeiyF16dspxXpywPO0a1k5AQtJYvXLeDcbPWhB1HROJMtEX57cBrwBNA0V0qXwDvA58Ct1Z+NBGR2Hj8s0UUuHP5cA1Ptzdem7qC16auCDtGtXRC79ZkNEvnwY8X4q7WchH5n6iKcncvcPdLCLqqXAXcDPwW6O/uZ7t7XgwziohUms3Zubzw1TJO6duGDk3rhh1HapnEBOOqw7swZ/U2Pp6rnp8i8j/RDonYFsDd57n7aHf/i7s/7O7TzCzJzP6vIic1s8vMbIGZ7TKzyWY2ZA/bDzWzT8xsi5mtMrNnzaxliW2GmdlXZrYzcuxLK5JJRGqHp75Yws7cAk3iIqE5tV8b2jWuw7/UWi4ixUTbfeVzM/vJ3VBmNhyYDtwZ7QnN7EJgFMFoLmcCW4D3Szt+ZPsewHhgO3Ae8Hvg4Mg+ycW2GQcsBs4A3gaeMLOzos0lIjXf1l15PDVpMcf3akW3lvXDjiO1VHJiAlcd1oVpy7fw+cINYccRkTgRbVG+gqAw7wFgZk3N7CmC4RBzgUOjOYiZGXAHMMbdb3f3d4FTgA3AtWXs9mtgNXCmu7/n7i8C5wJ9gaMj29wILAHOc/dx7n4dQdGvvu4i8oOnJy1he04+Vx/RNewoUsudOaAtrRqk8eDHC8OOIiJxItqi/GhgKjAx0lVlHnAacA1Bv/LPozxOF4Ixzd8qWhDpjz4WOK6MfWYB95botz4v8lzUun4U8I7/+HPAN4DeZtYmymwiUoNty8njic8Xccz+Ldm/TYOw41RrT19yIE9fcmDYMaq11KRELj80g68Xb+KrRRvDjiMicSDaGz1zCIrwt4E/E3RZ6ebuD7p7RaYm6xZ5Ltk0sAjINLPEUs79iLs/XGLxyZHnuWaWDrQp45jFzykitdizXyxhW04+vzlSreT7qk5KInVSfvLjWiro3EEdaFYvhYc+UWu5iEBSWSvM7IxSFo8F+gEHAmeY2fqiFe7+ehTnK2qe2l5i+XaCPxDSgW3lHcDM2gP3AFOAj4FW5Ryz+DmLH2MkMBKgQ4cOUcQWkepsx+58Hv98MUfu14JebRuGHafae27yEgBGDOkUao7qrk5KIr8clsHd783l++Vb6Ne+UdiRRCREZRblBOOSl+fRYl87EE2ziRXbvrTl5ba6Rwry8QQF/Lnu7pF+6hU6pruPAcYADBw4ULe+i9Rwz05ewpadeWolryRF08SrKN93FwzuyKiJWTz08QIev2hQ2HFEJETlFeWxmHt6a+S5PrC22PJ6BMVzdlk7mlkv4D0gGTja3bMiq4pa1ksOpVCvxDlFpBbK3p3P458t5rDuzemrlkiJM/VSk7j04M7c9+F8Zq7cqk9yRGqxMvuUu/vSijyiPN+CyHNGieUZwLwSN2r+wMwOIpg5tAAY5u7Ti+XcQTA6S2nHBJgfZTYRqYGe/3Ipm7JzNeKKxK2LhnaifloSD4xfsOeNRaTGinbyoEQz+5WZvWZmH5nZxyUe46M83wJgOcFNo0XHTgZOJOiWUtq5OxG0kK8Fhrp7aT+1xgMnl7hR9DRgpruvLWV7EakFduUWMObTRQzr2owBHRuHHUekVA3rJHPZsAw+nL2WGSv04a5IbRXtkIj/AB4EuhJ0Mdla4lHuzZlFIi3hdwNXmNldZnYC8CbQDLgfwMwyzWxwsd0eILhZ8w6gg5kNLvZoHdnmHqA78KqZHW9m9wIXRPYRkVrqha+WsjE7l9+qL7nEuUsO7kTDOsn88yN9uCtSW5XXp7y4EcCf3X2fJ+Nx90fMrA7wW4IJg74HjnX3oiEMbwEuIphrKBk4geAm0hdLOdz1wD3uPs3MTgb+BvwXWAZc4u6v7mteEamecvIKGP3pIoZmNmVgpyZhx6lRXr58SNgRapz6acmMHJ7BP96fp5FYRGqpaFvKUwmGH6wU7n6vu3dw97ruPtTdJxdbd7G7W+TrPHdPdncr43FPsf3ed/d+7p7m7t3c/enKyisi1c+LXy1j/fbdGnFFqo2LhnaicV21lovUVtEW5e8Ap8cyiIhIZdmZm88jE7IYnNGEwRlNw45T44z5NIsxn2bteUOpkHqpSYwcnsmEeeuZunRz2HFEpIqVN3nQdcVeLgZuMLMuwGRgZ4nN3d3vj0E+EZEKe3byUjbs2M2oC/qHHaVGGj9nHQAjh2eGnKTmuXBIRx7/bBH//Gg+z/3ioLDjiEgVKq9P+T2lLDs+8ijJidyoKSISpu05eYyamMVh3ZurL7lUO+mpSVx+aAZ/eXcu3yzZxCBdwyK1RnnjlCdU4BHNbJ4iIjH35OfB7J2/O7p72FFE9sqIwZ1oVi+V+z9U33KR2iTaPuWY2VAzu7HY635m9ryZHRCbaCIiFbNlZy6Pf7aIY3u2pHc7zYwo1VOdlESuPCyTL7I28uWijWHHEZEqEu3kQacCE4Fjii12gnHLvzCzwyo9mYhIBY35dBE7cvO59uhuYUep0dKSE0lL1geksfTzgzrQon4q9304nzImuxaRGibalvLbgMfd/YiiBe4+zd0PAp4hmBBIRCQ0G3bs5qlJSzi5Txv2a9Ug7Dg12jOXHsgzlx4YdowaLS05kasOy+TrxZv4Ikut5SK1QbRFeTfglTLWvQL0qpw4IiJ759EJWezOL+CaozQuudQM5x7YgTYN0/j7uLlqLRepBaItylcDg8tYNwDYUDlxREQqbs3WHJ77ciln9m9HRvN6Ycep8f41fgH/Gr8g7Bg1XlpyItcc3Y1pK7by/qw1YccRkRiLtih/ErjVzP7PzPqYWSsz621mNxF0bXkiZglFRPbgoU8W4O6avbOKTFq4gUkL1RZTFc44oC1dWtTjH+/PI7+gMOw4IhJD0RbldwOPAbcD3wErge8jr58A/hyLcCIie7J0YzYvf7Occwa1p32TumHHEalUSYkJ/P6Y7mStz+b1b1eGHUdEYiiqotzdC939N0AL4CRgBHAK0Nbdf+Pq7CYiIbn3g/kkJSTwmyPUSi4107E9W9KvfSPu/2g+OXkFYccRkRiJepxyAHff7O7vufuL7j7W3dfHKpiIyJ7MXLmVt6at4pfDOtOiQVrYcURiwsz4w3H7sXprDs9NXhp2HBGJkTKLcjPbZmYDIl9vj7wu67G16iKLiAT+Nm4ujesmM3J4RthRapXGdVNoXDcl7Bi1ypDMpgzv1pyHJyxkW05e2HFEJAaSyll3L8GoK0Vfq4uKiMSNzxas57MFG7j1pP2pn5YcdpxaZdSIAWFHqJVuOLY7Jz34OY99uojfHdM97DgiUsnKLMrd/fZiX99WJWlERKJQWOj8bdxc2jWuw88Hdwg7jkiV6NW2ISf1ac3jny3mwiGdaF4/NexIIlKJyizKzeyMChzH3f2/lZBHRGSP3pmxmpkrt3H/OX1JTdJ071Xtb+PmAvCH4/YLOUnt87tjuvPezDU8+PEC7jhV8/aJ1CTldV95rQLHcUC/GUUk5nLzC7nn/Xn0aN2AU/u2DTtOrfTt0s1hR6i1OjdL59xB7Xnxq2VcPLSTJssSqUHKG32lcwUeustKRKrEv79exrJNO/nDcd1JSLCw44hUuWuO6kZqUgJ/fW9u2FFEpBKV16dc4y6JSFzZuiuPB8YvYEhGUw7t1jzsOCKhaF4/lasO78I/3p/Hl4s2MjijadiRRKQSRDVOuZklmNnlZvammX1kZh+XeIyPdVARkYc/Wcjmnbn88cQemKmVXGqvXxzSmTYN0/jz2NkUFmpwNJGaINrJg+4FHgXaAdnA1hKPbTFJJyISsXRjNk9NWsxZ/dvRq23DsOPUaq0bptG6oSZrClNaciLXH9edmSu38cb3K8OOIyKVoLwbPYu7ALi9+DCJIiJV6a/vziU5MYHrj9X4zGH757kHhB1BgFP7tuWpSUv4x/vzOL5Xa+qkaLwFkeos2pbyVODTyjqpmV1mZgvMbJeZTTazIVHuV9/MlprZWaWsm2lmXuKxobIyi0h4vly0kXGz1nDloZm0aKAWWhGAhATjjyf0YPXWHJ74fFHYcURkH0VblI8FTquME5rZhcAo4HngTGAL8L6Zdd7DfvWBN4GfzBRiZilAN+BGYEixx7GVkVlEwlNY6Px57GzaNEzjsuEa6Cke3P72LG5/e1bYMQQ4KKMpx/ZsyaMTsli3PSfsOCKyD6LtvjIOuN/MMoCvgJ0l1ru737+ng1hwZ9YdwJiirjBm9iEwD7gW+E0Z+x1KUMi3LOPQ+wPJwJvurjGiRGqQ/3y7gpkrt/HAuf1IS9bH8/Fg9irdRhRPbjy+B0fPmcj9H87nr2f0CTuOiOylaIvypyLPJ0YeJTmwx6Ic6AJ0BN76YUf3PDMbCxxXzn5vAB8CFxH8UVBSHyAHWBBFBhGpJrJ35/OP9+fRr30jTunbJuw4InGpc7N0LhraiScnLeb8AzvSu51uhBapjqLqvuLuCXt4RNt81S3yvLDE8kVAppmVdZxh7v4zYF0Z6/sAG4GXzWybmW01s8cjXV5EpJoaPTGLddt3c8tJ+2sIRJFy/PaorjRNT+FPb83UEIki1VS0fcorS4PI8/YSy7dHsqSXtpO7z9zDcfsArYBpBC35NxP0V39jb4OKSLiWbsxm1KeLOKVvGwZ0bBx2HJG41iAtmRuO249vl23REIki1VSZ3VfMbBtwuLtPNbPtBF1UyuTuDcpbX3TYos3LWF4YxTFK8wcg1d2/jLz+zMzWAS+Z2TB3/+xHJzMbCYwE6NDhJ/eNikgcuOPt2SQnGH88sUfYUaSEjOaltp9IyM7q344XvlrGX9+by9H7t6R+WnLYkUSkAsrrU34vsLrY15XxedjWyHN9YG2x5fUICvLsvTmou39XyuJxkee+wI+KcncfA4wBGDhwoD7nE4kz4+esZfzcddx0/H601BCIcUc3E8anhATj9lN6ctrDk3jw44X83wn6g1akOimzKC8+UZC731ZJ5yu6ETODH/crzwDmuXuFC2QzSyKY3GhaieK8TuRZY5WLVCM5eQXc/vZsMpunc8nB5Y6UKiIl9GvfiJ8NbMeTny/mZwPb06VFvbAjiUiUou5TbmYNzexmM/vEzOaYWU8z+4OZVWQs8AXAcoqNeW5myQT9wMdX4Dg/cPd84HbgthKrzgTygMl7c1wRCceYTxexbNNO7ji1FylJVX3bi0Tjptenc9Pr08OOIWW44bj9qJOSyO1vz2Iv2rpEJCRR/cYzs07ADOA6YBvBKCqpBDdYvmNmx0dznEhL+N3AFWZ2l5mdQDAhUDMiQyqaWaaZDa7g93EXcIqZPWBmR5nZTcA9wL/cfWkFjyUiIVm+aScPf7KQE3u35uAuzcKOI2VYtD6bRev3qrehVIFm9VK59qhufLZgAx/MXrvnHUQkLkTbDPUAQf/yDgQt0Abg7j8H/gvcGu0J3f0R4HpgBPAa0Ag41t2L5gi+hQq2bkf6iF8CHA68TXAT553ADRU5joiE6853ZpNgurlTZF+NGNKR7i3rc8fbs8nenR92HBGJQrRF+RHAX9x9Bz+94XM00KsiJ3X3e929g7vXdfeh7j652LqL3b3UAYndfYm7m7u/Vsq6p929j7vXcffO7v4Xd9/b0VxEpIpNmLeOD2av5eoju9CmUZ097yAiZUpOTOCu03uxcssu/vnR/LDjiEgUoi3Kc/nfjZMlNQF2V04cEamNduUWcMubM8lons4vDtHNnSKVYWCnJpx3YHuenLSEWau27nkHEQlVtEX5WODPZta12DI3sybATcD7lZ5MRGqNf46fz/JNu/jL6b1JTYp2gmAJy/5tGrB/m2imppCw/eG4/WhcN5n/++9MCjTTp0hci7Yo/x1Ba/gsoOiW+yeALKAhQR9xEZEKm7VqK49/tphzB7VncEbTsONIFP50ck/+dHLPsGNIFBrVTeHmE/dn2vItvPiVxj0QiWdRFeXuvh4YAFxNUJR/RFCQ3wb0c/dVsQooIjVXQaFz0+szaFw3mZuO182dIrFwar82HNKlGX8fN4+123LCjiMiZYh6EGB3z3H30e5+nrsf4+5nu/sD7r49lgFFpOZ6dvISpq/Yyq0n96RhXU0JXl1c89J3XPNSaRMpSzwyM/58Wi92FxRyxzuzw44jImUoc0bPksysF3AYwRCGJYt5d/c7Ky+WiNR0K7fs4h/vz+Ow7s05uU/rsONIBazeqtbW6qZTs3SuPrwL9344n7P6r+Pw/VqEHUlESoiqKDezXxAMfZgAbAdKDjXoBOOCi4jskbtz6xszcYc7T+2FWamjoIpIJbr80Ezenr6K//vvDN6/djgN0vTplEg8ibb7yv8RTMrT1N0bunvjEo8mMcwoIjXM2BmrGT93Hb87phvtm9QNO45IrZCSlMA/zurL2m05/GXsnLDjiEgJ0RblbYAH3X1zLMOISM23Ycdubn1zFn3aNeTioZ3CjiNSq/Rt34iRwzN56ZvlfDp/fdhxRKSYaIvyKcD+sQwiIjWfu3PLGzPZkZPPPWf3JSkx6nvNJY7079iY/h0bhx1D9tI1R3Uls3k6N70+g+05eWHHEZGIMvuUm1n/Yi+fBu4zszrAZGBnye3d/dtKTyciNco701fz3sw1/OG4/ejWsn7YcWQv/eG4/cKOIPsgLTmRf5zdl7Me/YK/vjeXv5zeO+xIIkL5N3pOIbiBs4gBfyuxrGi5A5qGT0TKtH77bm59cyZ92zfismGdw44jUqv179CYXw7LYMynizixd2sO7tIs7EgitV55RfnhVZZCRGo0d+fmN2aQnVvAvWf3UbeVau6K56YCMGrEgJCTyL647uhufDR7LTe8Np33rx1OvdSoR0kWkRgo8zeju08s/gC+B5KKvV4CdAW+jbwWESnVW9NW8f6stfzu6G50aaFuK9Xd5p25bN6ZG3YM2UdpyYn8/aw+rNq6i7vGalIhkbBF1VwVmThoDjCm2OLOwIPAt2bWqfKjiUhNsGrLLm55Yyb9OzTil8Mywo4jIsUM7NSEKw7N5N9fL+eDWWvCjiNSq0X7GfK9wEJgcNECd59AMFTiKuD+Sk8mItVeQaFz7cvfU1Do3H9OPxITNEmQSLy59qhu9GzTgBtfn8G67ZqtVSQs0RblBwF3uvuPBjWNjFt+N3BoZQcTkepvzKeL+GrxJm47pScdm6aHHUdESpGSlMAD5/Yje3c+N7w2HfeS4zmISFWItijPIWgVL01ToLBy4ohITTFjxVbu+3AeJ/ZuzVkD2oUdRyrRwV2aabSOGqZLi/r88cQeTJi3nue/XBp2HJFaKdpbrd8B7jKzBe7+RdFCMxsC3AW8FYtwIlI97cot4Lcvf0fT9FTuOr0XZuq2UpP85siuYUeQGBgxuCPj56zjz2PnMCSzqW7KFqli0baUXw+sAz4zs01mNtfMNgKfAxuA38cqoIhUP38eO5vFG7K575y+NKqbEnYcEYmCmfGPs/uQnprE1f/+npy8grAjidQqURXlkb7jg4AzCEZg+RR4EjgLOMjdN8UsoYhUK+9MX8ULXy1j5LAMhmaqi0NNdNGTX3PRk1+HHUNioEX9NO49uy9zVm/jznc0TKJIVYp6pgB3LwDejDwwsySgobvnxyibiFQzSzZkc+N/ZnBAh0b8/tjuYceRGFELas12+H4tuHx4BqM/XcSQzKac1KesW8pEpDJFO055qpndZWYXRF4PJejOss7MJpiZmsNEarmcvAKueuFbEhOMh87vT7Jm7RSptn5/bHf6d2jEjf+ZwdKN2WHHEakVov2t+VfgWiA58vpZYAVwCdAKuKfyo4lIdXLnO7OZvXob9/2sL20b1Qk7jojsg+TEBB48vz+JCcavXvyW3fn6dEQk1qItys8GrnX3p8xsEJAB/NndnwVuBk6syEnN7DIzW2Bmu8xscmQUl2j2q29mS83srFLWDTOzr8xsZ+TYl1Ykk4jsvbemBf3ILx+ewZE9WoYdR0QqQdtGdbjn7L7MXLmNv4ydE3YckRov2qK8GVB0x8dJQB7wXuT1JiAt2hOa2YXAKOB54ExgC/C+mXXew371CfqzdyhlXQ9gHLCY4GbUt4EnSiveRaRyZa3fwU3/mc6Ajo3Vj7yWOLJHC47s0SLsGFIFjt6/Jb84pDPPTF7Kf79bEXYckRot2hs9s4CDzexL4GfA5+6+PbLuXGB+NAexYLDiO4Ax7n57ZNmHwDyC7jG/KWO/QwkK+bKa4G4ElgDneTAV2Tgzaw7cCrwWTTYRqbjtOXmMfHYKacmJPHjeAepHXkuMHJ4ZdgSpQjcevx8zV27lptdn0K1lfXq2aRh2JJEaKdrfoP8A/gysB7oB9wGY2WTgUuDuKI/TBehIscmG3D0PGAscV85+bwAzytnmKOAd//HcwG8Avc1Mt42LxEBhoXPdK9NYsnEnD53fnzbqRy5SIyUnJvDQ+f1pVCeFy5+byubs3LAjidRI0Y5T/gxwCEFhPtzdx0ZWjQOOcPdXozxft8jzwhLLFwGZZpZYxn7D3P1nBCO+/IiZpQNtyjhm8XOKSCV68OOFfDh7LTef2IMhmU3DjiNV6JzRkzln9OSwY0gVal4/lUcv6M+6bbv5zUvfUVDoe95JRCok2iERXwRS3f0ed59UtNzdb3f3TytwvgaR5+0llm+PZEkvbSd3n7mXxyy+/gdmNtLMppjZlPXr15efWER+4qPZa7n/o/mc0b8tFw/tFHYcEakCB3RozO2n9uSzBRu454N5YccRqXGi7b5yYgW2LY9Fnkv+iV20vLAqjunuY9x9oLsPbN68+V6cUqT2ylq/g2tf/p7ebRvyl9N7E9wqIiK1wXkHduC8A9vz6IQs3vx+ZdhxRGqUaAvtd4BfmVnjfTzf1shz/RLL6xEUz3szQ8G2co5Z/Jwiso82Z+fyi6e/ISUpgVEjBpCWXFaPMxGpqW47pScHdmrC9a9NZ+rSzWHHEakxoi3K6wKnABvMbI2ZTS/xmBblcRZEnjNKLM8A5pW4UTMq7r4DWF3GMSHKkWFEpHy78wu4/LmprNqaw5gLB2iCIJFaKjUpkVEjBtC6YRqXPzeF5Zt2hh1JpEaItijfArxAMJPne8DUEo9vozzOAmA5cFrRAjNLJugeMz7KY5RmPHByiRtFTwNmuvvafTiuiADuzk3/mcHXSzZxz9l9GdCxSdiRJEQn9WnNSX1ahx1DQtQkPYUnLhrE7vxCfvnMFLbn5IUdSaTai2qccne/pDJO5u5uZncDD5nZZmAS8GuCyYnuBzCzTKC5u39ZgUPfA3wDvGpmjxEMkXgBwZjqIrKPHvp4Ia9/t5LfHd2NU/pqlNHabsSQTmFHkDjQpUU9Hv35AC566muu/vd3PH7hQJI0V4HIXov6f4+ZJZhZLzM7xMyGl3xEexx3fwS4HhhBMLFPI+BYdy8awvAWoEJjbbn7NOBkgi4r/418fUkFhmoUkTK8NW0V9344nzMOaMuvj+gSdhyJA7tyC9iVWxB2DIkDh3Rtxh2n9mTCvPX86a1Z7EUvVBGJsGj+A5nZEOA/BDNqljbUgrt7tbzja+DAgT5lypSwY4jEpUkLN3DxU19zQPvGPPfLA0lNqpb/zaWSFY1R/vLlQ0JOIvHi7vfmMmpiFtcd3Y3fHNk17DgiccvMprr7wNLWRdV9BfgXQb/yXxFMZ783QxeKSDUyc+VWRj47hYxm9XjswoEqyEWkTH84rjvrtudw34fzaV4/lfMO7BB2JJFqJ9qivBdwVrGZPEWkBluyIZuLn/qaRnVTeObSA2lYNznsSCISx8yMv53Zh407cvnjf2fQrF4qR+/fMuxYItVKtH3KlxIMiygiNdy6bTmMePIrCh2e/cWBtGqYFnYkEakGkhMTeOTn/endtiG/fvFbpizZFHYkkWol2qL8VuAuMxsUyzAiEq4tO3O56Klv2Lgjl6cuHkRm83p73klEJCI9NYknLx5E20Z1uOSpb5ixQvP3iUSrzKLczLab2TYz2wY8DmQCX5pZbtHyYg/9rxOp5rbl5HHhk1+TtW4Hoy4YQN/2jcKOJHHqrAHtOGtAu7BjSJxqWi+V5355EA3qJDPiya+Yu2bbnncSkbJHXzGz24CoxzZy99srKVOV0ugrIrBjdz4XPvEV01dsZdQFAzhKfUFFZB8t27iTn42eTH5hIS+NHEKXFvrkTaS80VeiGhKxJlNRLrXdrtwCLn7qa6Ys3cxD5x3A8b01U6OUb1N2LhDM6ihSnqz1Ozhn9GQSE4xXLh9Cx6bpYUcSCVV5RXlFJg9qamYnmNnpZnZG5HGmmY0ws0cqL66IVJWcvAIue3YK3yzZxH0/66uCXKJy5fNTufL5qWHHkGogs3k9nv/lQezOL+T8x75i6cbssCOJxK2oinIzOx1YDrxDMAvnq5HnV4CngcNjlE9EYiR7dz6XPv0Nk7I28Pez+nJqv7ZhRxKRGmi/Vg14/hcHkZ2bzzmjvyRr/Y6wI4nEpYqMvvIt0B94EngB6AlcD+QC18YknYjExLacPC568mu+XLSR+37WVzftiUhM9WrbkJdGDiavoJBzRn/J/LXbw44kEneiLcr3A/7m7t8DHwP93H2Ou98H3APcHKN8IlLJtuzM5YLHv+L75Vt46Pz+nH6ACnIRib39WjXg5csHk2Bw7pgvmbVKA7eJFBdtUZ4HFP1ZOx/obmZFU/yNB3pUdjARqXzrt+/m3DFfMnfNdsZcOIAT1IdcRKpQlxb1eeXyIaQlJXD+Y18xdenmsCOJxI1oi/JvgTMiX88BDBgWed2hskOJSOVbujGbs0d9wdKNO3nq4kEcsZ+GPZS9c8HgjlwwuGPYMaSa6tQsnZcvH0Ljusn8/PEv+Xju2rAjicSFaIvyvwJXmdlL7r6T4AbPF83saeCfwEexiScilWHGiq2c+egXbN2VxwuXHcTBXZqFHUmqsZP7tuHkvm3CjiHVWPsmdXntyqF0bVGfy56dyitTlocdSSR05c3oOdnM7jSzw4BPgCHAuMjqkcC7wIHA28CvYhtTRPbWxPnrOWfMZFKTEnntyqH079A47EhSza3asotVW3aFHUOquWb1Uvn3yMEMzWzKDa9N55EJC6ntc6dI7VZeS/lmgmL7Y2AL8BeglZkNAna5+6Xuvr+7X+TuG2IfVUQq6j9TV/CLp7+hY9N0/nvVUDKba0Y92XfXvvw91778fdgxpAaol5rEExcN4pS+bfj7uHnc8uZM8gsKw44lEoqksla4+wlmZgRDHw4DhgKXExTnW81sAsFNnuPdfU4VZBWRKBUWOvd8MI9HJmQxNLMpo0cMoH5a8p53FBGpYilJCfzznH60bpjG6E8XsXTjTh46vz8N6+hnltQu5fYp98BMd3/U3Ue4e2egHUFxvhwYAXxvZiurIKuIRCF7dz5XPD+VRyZkcd6B7Xn6kgNVkItIXEtIMG46oQd/P7MPk7M2csYjkzT7p9Q60d7oCYCZJQEZQBcgE2gNJAJrKj+aiFTUyi27OGvUZD6YvZaOTeryl9N7k5JUof/mIiKh+dmg9nRtWY8lG3dy2sOT+GrRxrAjiVSZPf62NrP9zey3ZvYOQT/zT4FfACuA3wEt3H1AbGOKyJ58uWgjpz70OSs27aR7q/q0aphG0ANNRKT6aJCWTK82DWicnsLPH/+KJz9frBtApVYos095ZLjDowhawzcSjMByHfChuy+pinAismfuzphPF/H39+fRsUldRl82gKUbd4YdS2qwy4ZlhB1BarCi6+vAjCb87pVp3PHObL5dtpm/ndmH9NQyyxaRas/K+uvTzAoJivEHgIfcfUsV5qoyAwcO9ClTpoQdQ2SvbMvJ4/evTOOD2Ws5oXcr/nZmH/UfF5Eao7DQeXRiFvd+MI/M5vUYNWKARpGSas3Mprr7wNLWldd95Sbgu8jzOjP7wszuMLNhkb7lIhKiOau3ccqDn/Px3HXcctL+PHx+/x8K8qz1O8havyPkhFJT6fqSWCp+fSUkGL86vAvPXnoQG7NzOfWhSbw7Y3XICUVio8yW8h82MEslGBLxSOBooB+wi6Bv+YfAR+4+M7YxY0ct5VLduDvPTl7KX96dQ6O6yTx8fn8Gdmryo23OGT0ZgJcvHxJGRKnhdH1JLJV1fa3csourXviWacu3cM7A9vzplP2pm6I2Qqle9ralHAB33+3uH7n7TZGDtAAuBZYClxAMibiqgoEuM7MFZrYrMnNouT/ZzayXmY03sx1mtszM/mAl7mAzs5lm5iUemtRIapT123dz6dPf8Ke3ZjE0synvXD3sJwW5iEhN1LZRHV67YghXHZbJK1OXc9K/PmfGiq1hxxKpNBUdEtGA9kBTIA3wyKOgAse4EBgFPA+cSTBb6Ptm1rmM7VsAH0XO8zNgDHAXwcgvRdukAN2AG4EhxR7HVuT7E4ln4+es5bh/fsoXWRu549SePHnxIJrXTw07lohIlUlOTOCG4/bjxV8OZmduAWc8OonRE7MoLNToLFL9lfu5j5k1BQbzvyJ3EJBOMC75ROBh4BN3XxjNySJF/R3AGHe/PbLsQ2AecC3wm1J2+1Uk5ynuvhN4N9Kl5iYze8Dd84D9gWTgTXefG00Wkepix+58/vruHF74ahk9WjfgpXP70bVl/bBjiYiEZkhmU8ZdM4ybXp/BX9+by/i56/j7mX3o1Cw97Ggie628IRHnE0wQZMA6YAJwA0ERPm8vz9cF6Ai8VbTA3fPMbCxwXBn7HAWMjxTkRd4Abib4I+ELoA+QAyzYy1wicWni/PX83+szWLV1F5cN68zvj+1OalJi2LFERELXqG4Kj/y8P69NXcEd78zmuAc+5ffHdOeSgzuTmKA5GqT6Ka+lfBrwT2CCu8+upPN1izyXbFlfBGSaWaK7l+wK043gD4KS2xetKyrKNwIvm9kxBF1dXgWudfftlZRdpMps2ZnLne/M4T/frqBLi3q8dsVQBnRsHPX+Vx/RNYbppLbT9SWxVJHry8w4e2B7hndrzh//O4M/j53DuzNW8/ez+tKlhYZOlOqlzKLc3c+OwfkaRJ5LFsrbCfq3pwPbStmntO2LH68P0IrgD4kHCEaIuQPoTDBqzI+Y2UhgJECHDh0q+C2IxI678+6MNfzprVls2ZnL1Ud04ddHdKlw6/ghXZvFKKGIri+Jrb25vlo2SOOxCwfy5veruO3tWZzwr8+46rBMrjg0k7Rkfboo1UNVjyVU9HlSyTsyipYXlrFPWXdwFG3/ByDV3b+MvP7MzNYBL5nZMHf/rPhO7j6G4IZRBg4cqLtDJC4sXLeD296axecLN9CzTQOeuXQQPds03KtjzVoVjEiwt/uLlEfXl8TS3l5fZsZpB7RlaJem3P72bP750QL++91KbjulJ4d3bxGLqCKVqkKjr1SCorGLSt6lVo+gwM4uY5+S29cvtg53/65YQV5kXOS5795FFaka2bvz+et7czj+gU+ZtmILt5/Skzd/dfA+FTx3vD2bO96urF5nIj+m60tiaV+vrxb103j4/P48/4uDSDTjkqe+4fLnprByy65KTClS+aq6pbzoRswMftyvPAOY56XPZLQgsp4S2wPMi8wuegEwzd2/K7ZNncizxiqXuFRY6Lw9fRV/fXcua7blcPaAdvzh+P1oVk/DHIqI7KtDujbjvWuG8fhni3nw4wUcde9ERg7PYOTwDNJTNemQxJ8wivLlwGnABwBmlgycCIwtY5/xwOVmlu7uRS3ppxHc2Pm9u+eb2e3A98CpxfY7E8gDJlfutyCy777I2sBf353LjJVb6dmmAQ//vH+FbuQUEZE9S01K5FeHd+HUfm3467tzeWD8Al78ehm/O7obZw9sr1FaJK5UaVHu7m5mdwMPmdlmYBLwa6AZcD+AmWUCzYt1R3kEuJpgfPJ/EHRHuQm40d1zI9vcBYw2sweAtwmGSrwV+Je7L62a705kz+av3c7d783l47nraNuoDvef05dT+7YlQb8YRERipl3jujz88/5cunQTd42dw42vz+CpSUu48YT9OKxbc0pMEi4Siir//MbdHzGzOsBvCSYM+h441t2Lhjm8BbiIyM2f7r7azI4iGFXlNWAt8Ed3v6fYMceYWS5wHcGoKmuAO4G7q+SbEtmDJRuy+dfHC3jju5WkpyZx0/H7cdHQThoVQESkCg3o2IT/XDmU92au4e735nLJU98wsGNjrju6G0Mym6o4l1BZ6d24a4+BAwf6lClTwo4hNdSSDdk8+PFC3vh+JcmJxgUHdeRXh3ehcXpKTM87dekmIPgFJFLZdH1JLFXV9bU7v4CXv1nOw58sZO223RzUuQnXHt2NwRlNY3peqd3MbKq7Dyx1nYpyFeVS+RZvyOahEsX4yEMzaFE/LexoIiJSTE5eAS99vYxHJmSxbvtuhmQ05TdHdmVwRhO1nEulU1FeDhXlUpm+XbaZxz5dxLhZa0hNSgitGFdLpsSSri+JpbCur5y8Al78KijON+zYTZ92DRk5PIPjerYiKbGqR5CWmkpFeTlUlMu+Kih0Ppqzlsc+XcSUpZtpkJbEBYM7cvHBnUJrGT9ndDDo0MuXDwnl/FKz6fqSWAr7+srJK+D1b1fy2GeLWLwhm/ZN6vDLQzI4e2A76qZoKEXZN+UV5bq6RPbS1l15/PfbFTwzeSmLN2TTrnEd/nTy/vxsYHuNgSsiUk2lJSdy/kEdOGdQez6cvZbRn2bxp7dmcf9H8/nZwPZccFBHOjStG3ZMqYFUOYhU0IwVW3n+y6W8NW0Vu/IK6Ne+EQ+df4A+4hQRqUESE4zjerXi2J4tmbJ0M09+vpgnPl/MY58t4tBuzblwSEcO7dZCY51LpVFRLhKFHbvzeXf6al74ainTVmylTnIip/ZrwwWDO9KrbcOw44mISIyYGYM6NWFQpyas2ZrDi18v499fL+PSp6fQrnEdzh3UntP7t6Ntozp7PphIOVSUi5ShoND5ImsD/5m6gnGz1pCTV0iXFvW47eT9Ob1/OxrWSQ47ooiIVKFWDdO47uhuXH1EFz6YtZbnvlzCPR/M594P5zM0sylnDWjHsT1bqe+57BXd6KkbPaWEBWu38/p3K/nvtytZsy2HBmlJnNS3DWf2b0f/Do2qxRBZs1ZtBaBnG7XiS+XT9SWxVN2ur+WbdvKfb1fwn29XsHzTLtJTEjmxT2tOO6AtB3Vuqu4t8iMafaUcKsoFYP7a7Yydvpr3Zq5m/todJCYYh3Zrzpn923FkjxaaeVNERMpVWOh8s2QTr01dwbszVpOdW0Czeqkc36sVJ/RuzYGdm6hAFxXl5VFRXju5O3PXbOe9Gat5d+YaFq7bgRkM6tSEE3q14sQ+bWhePzXsmHvt8wUbADika7OQk0hNpOtLYqkmXF+7cgv4ZN46xk5fzfi5a8nJK/yhQD++VysGdW5CsgYGqJU0JKIIwdizk7M2Mn7uWj6Zu56VW3aRYHBg5yZcNKQnx/ZqVWNm3Hzw4wVA9f6lJvFL15fEUk24vuqkJHJC79ac0Ls1O3Pz+WTuesbOWMWrU5fz3JdLqZ+axPDuzTlyvxYc1r0FTdJTwo4scUBFudRoKzbvZMK89Xwydx2TsjaQk1dI3ZREDu7SjF8f0YWjerSs1i3iIiIS3+qmJHFin9ac2Cco0D9fsIGP565j/NygJd0M+ndozBH7teDQbs3Zv3UDEtTNpVZSUS41yvrtu5m8aCOTszbwRdZGlm7cCUD7JnU4d1AHDt+vBQd1bqI+4iIiUuXqpiRxTM9WHNOzFYWFzsxVWxk/Zx0fz13HP96fxz/en0ejuskMzWzK0MxmHNKlGR2b1q0WAwzIvlNRLtXaxh27mbJ0M5OzNjI5ayPz1m4HoH5aEoMzmnLx0E4M69qMzOb19ENNRETiRkKC0addI/q0a8S1R3dj3bYcJmVtYNLCjUxauIF3Z6wBoG2jOgzNbMqgzk0Y2LExnZul6/dZDaWiXKqNwkJnwbodTF26malLN/Ptss0s3pANQFpyAoM6NeG0A9oyNLMpPds00OyaIiJSbbRokMbpB7Tj9APa4e4s3pDNpIVBkf7B7LW8OnUFAE3TUxjQsTGDOjVhQKfG9GrTkJQk/b6rCTT6ikZfiUvuzqqtOcxYsZVZq7YybcVWvlu2me05+UDwQ6l/x8YMiDz6tGtIapK6pBTJWr8DgMzm9UJOIjWRri+JJV1fP1VY6GSt38GUpZv5Zskmpi7d/EP3zNSkBHq2aUDvtg3p3a4Rfdo1JLN5PQ2/GKc0JGI5VJSHz91ZsXkXM1ZuZebKrcxYuZVZq7axKTsXgASDbi3rB0V4h6AIVx87ERGpzdZtz+HbpZuZsmQz01dsZeaqrezMLQCgTnJiUKi3a0jvtg3p0boBGc3T1XgVB1SUl0NFedVxd9Zt3838tduZt2Y7C9buYN7a7SxYu53syA+SpASja8v69G4b/NXfs21DerRqQJ0U/SCpiI9mrwXgqP1bhpxEaiJdXxJLur72TkGhs3jDDqav2BoU6SuDQj0nrxAIfr92bpZO91b16d6yPt1b1We/Vg1o17iORnupQhqnXKrU7vwClm3cyeIN2SzZmM3iDTvJWhcU4Ft35f2wXdP0FLq1rM9ZA9rRrVV9erVpSPdW9TUySiV47LNFgH6pSWzo+pJY0vW1dxITjC4t6tOlRX3O6N8OgPyCQrLWZzN3zbYfGsSmrdjCO9NX/7Bf3ZREurSoR0azdDo1S6dzs3QymtWjU7O61E9LDuvbqZVUlMte2Zmbz8rNu1i26X/F95INwdertu6i+Acwjesm06VFPU7s05ruLevTtWU9urWsT7N6Gh9cREQkVpISE4KW8Vb1f7R8x+58FkSK9LlrtrNw3Q6+WbKZN6et+tHv7+b1UyNFelCwt29cl3aN69CucR2apKeoG2klU1EuP+HubNmZx8otu1ixeRcrt+xi5eZdrNyy84evN+/M+9E+DdKS6NwsnYGdGtOpaTs6F/3F3TSdhnX1l7aIiEi8qJeaxAEdGnNAh8Y/Wp6TV8DSjTtZvGEHizZks3h9Nos3ZPPh7LVsjNznVaROcuIPBXr7JkXFel3aNKpDqwZpNKuXolHQKkhFeS3i7mzfnc+6bbtZty2Hddt3s7bEc9HyoptFitRJTqRt4zq0bVSHPu0a0bZRnR/+A3Zulk7jusn6i1lERKQaS0tOLLVlHWBbTh4rNweNdcs37WTF5l2s2Bw8T126mW2R0dGKJBg0q5dKq4ZptGyQRqsGabRqmEaL+sGyVg3SaFE/jQZ1klQ/RKgor8bcnV15BWzckcum7Fw27cxlU4mvN2bnsnlnLht27Gbdtt3syiv4yXHqpiTSskHwH6V3u0a0qJ9K64ZptGtch7aN6tK2cR0V3SIiIrVYg7RkGrROpkfrBqWu37orjxWbd7J6Sw5rtuWwNvJYs203yzbu5OvFm350X1mR5ESjSXoKTdNTaVovhWb1UoPX9VJoFlnWtF4qTdNTaJKeQt2UxBpbj4Qy+oqZXQbcALQDvgeuc/fJ5WzfC3gAOAjYBDwM/N2LhTezYcA9QG9gJfBXd39yT1niYfSVnLwCtuXksW1XPlt35UW+jjxyIst25f2wbuuuvB8K7t35haUeMznRaFw35YcLu0l6Ki3rpwbFd4NUWtQPnls2SKNeqv42q2lWbdkFQJtGdUJOIjWRri+JJV1fNdeu3ALWbc9hzdagcF+/fTebsnPZuCOXjdm72RB53rgj9yef2BdJTjQa1kmhYZ0kGtVNoVGdZBrWSaZh3eC5UZ1kGtVN+dGyBmnJ1E9LiouBJOJq9BUzuxAYBdwBfANcDbxvZn3dfXEp27cAPgJmAj8D+gN3AQUERThm1gMYB7wN/Ak4BnjCzLa5+2sx/6YqqKDQOfafn/5QbJdVWBdJS06gQVrkwqqTTPN6qXRv2YCm9VJoXDflh78em9RLoUnd4Ll+qj4Oqs30y0xiSdeXxJKur5qrTkoiHZum07Fp+h633ZmbHynWc9kUKdg3ZeeydVceW3bmsXVX8PWabTnB6G4789i+O7/cY6YkJlA/LYn6aUn889wD6Ne+USV9Z5WjSotyC6rEO4Ax7n57ZNmHwDzgWuA3pez2K4Kcp7j7TuBdM0sFbjKzB9w9D7gRWAKcF2k9H2dmzYFbgbgryhMTjEZ1koPuIm0b0iBSbDdIS/qh8C76y65BnSQN9i8V9va0VQCc3LdNyEmkJtL1JbGk60sA6qYkUbdJEu2b1I16n/yCQrbl5LNlZ6R435UXFOs5Qc+D7Tn5zFi5hZzcQhqkxV8vgapO1AXoCLxVtMDd88xsLHBcGfscBYyPFORF3gBuBgYBX0S2ed5/3BfnDeACM2vj7qsq7TuoJIkJRkGhc9MJPcKOIjXQ818uBfRLTWJD15fEkq4v2VtJiQlBz4H0lDK3OWf0ZJISjYzm9aowWXSqeqyabpHnhSWWLwIyzay0JuFuZWwP0M3M0oE25W2zl1lFRERERKpEVRflRbfsbi+xfHskS2mdjBqUsX3RuvKOWfycIiIiIiJxqaqL8qI7D0sO+VK0vLQ7Hq2U7YsU7s0xzWykmU0xsynr168vP7GIiIiISIxVdVG+NfJcclT6egTFc3YZ+5Tcvn6xddvKOWbxc/7A3ce4+0B3H9i8efNocouIiIiIxExV3+i5IPKcwY/7gGcA87z0QdMXRNZTYnsi++wws9XlbDN/H/LGzKMXDAg7gtRgur4klnR9SSzp+pJYiufrq6pbyhcAy4HTihaYWTJwIjC+jH3GA0dFbugschqwkWDioaJtTi5xo+hpwEx3X1sJuSvdnu4OFtkXur4klnR9SSzp+pJYiufrq0pbyt3dzexu4CEz2wxMAn4NNAPuBzCzTKC5u38Z2e0RggmG3jWzfwB9gZuAG909N7LNPQQTEb1qZo8RDJF4AcFkQ3Hp1SnLATh7YPuQk0hNpOtLYknXl8SSri+JpXi+vqq6pRx3fwS4HhhBMLFPI+BYdy8awvAWYHKx7VcTFNlJke1HAn9093uKbTMNOJmgy8p/I19f4u6vxvr72VuvTV3Ba1NXhB1DaihdXxJLur4klnR9SSzF8/UVynRG7n4vcG8Z6y4GLi6xbApw8B6O+T7wfuUkFBERERGpOlXeUi4iIiIiIj+molxEREREJGQqykVEREREQmalDw1eewwcONCnTJlS5efdlVsAQJ2UxD1sKVJxur4klnR9SSzp+pJYCvv6MrOp7j6wtHWh3Ogp+mEjsaXrS2JJ15fEkq4viaV4vr7UfSUkz01ewnOTl4QdQ2ooXV8SS7q+JJZ0fUksxfP1paI8JO9MX80701eHHUNqKF1fEku6viSWdH1JLMXz9aWiXEREREQkZCrKRURERERCpqJcRERERCRkKspFREREREKmccpDGqdcRERERGqX8sYpV0u5iIiIiEjIVJSLiIiIiIRMRbmIiIiISMhUlIuIiIiIhExFuYiIiIhIyFSUi4iIiIiETEW5iIiIiEjIVJSLiIiIiIRMRbmIiIiISMhUlIuIiIiIhExFuYiIiIhIyFSUi4iIiIiETEW5iIiIiEjIVJSLiIiIiITM3D3sDKEys/XA0pBO3wzYENK5qyO9XxWj96ti9H5VjN6vitH7VTF6vypG71fFhPl+dXT35qWtqPVFeZjMbIq7Dww7R3Wh96ti9H5VjN6vitH7VTF6vypG71fF6P2qmHh9v9R9RUREREQkZCrKRURERERCpqI8XGPCDlDN6P2qGL1fFaP3q2L0flWM3q+K0ftVMXq/KiYu3y/1KRcRERERCZlaykVEREREQqaiPM6Y2W1mpo8vymFmx5rZN2aWbWYLzOxqM7Owc8UrMxtqZp+Y2RYzW2Vmz5pZy7BzxTszq29mS83srLCzxBMzuyzy/26XmU02syFhZ6oOzOwUM9sedo54ZmaJZnadmc2J/HyfbWa/1s/3splZipn9OfKzKtvMPjaz/mHnindmlhq5zp4OO0txKsrjiJn1Am4KO0c8ixQA7wAzgVOBx4D7gGtCjBW3zKwHMB7YDpwH/B44GHjfzJLDzBbPzKw+8CbQIews8cTMLgRGAc8DZwJbCK6lzmHmindmNpTgPVNxWb5bgL8QvFenAK8A/wSuDzFTvLsf+A1wN3A6sBP4xMw6hpoq/v0J2C/sECWpT3mcMLNE4AugLdDW3fXDuxRm9grQDTjAIxevmT0FDHP3LqGGi0Nm9jBwPNDd3fMiywYBXwMnuvu7YeaLR2Z2KEHh2RJoDJzt7q+Fmyp8kdbKxcB77n5lZFkyMA94x91/E2a+eGRmqcBvgTuBbCDF3euFmyo+mVkCwR95D7j7LcWWP0zwf7BFWNnilZk1BNYDN7r7fZFldYCNwF/c/c9h5otXZnYA8BmwCxjr7heHm+h/1FIeP64FGgAPhh0kzv0OOM9//NdkLpAaUp54Nwu4t6ggj5gXeVbrZuneAGYAx4WcI950AToCbxUtiFxXY9F7VZbjCT79vB79bN+ThsCzwOslls8DmptZetVHinvZwEHAU8WW5QGOfieWysySgCeBfwArQ47zE0lhBxAwsy7AbQS/2OJuhql44u7Li742s0YEH3FeCKhFoBTu/kgpi0+OPM+tyizVyDB3n2lmncIOEme6RZ4Xlli+CMg0s0R3L6jiTPHuG6Czu28xs9vCDhPP3H0z8OtSVp0MrHD37CqOFPfcPR/4Dn74pKEjcDtBUf58iNHi2R+AFOCvBN194oqK8hiKfLSbWc4mawk+rnsceM7dPzezWluUR/N+RX5wE+kvtySyfArwaGzTxZ+KvF/F9mkP3EPwnn0cw3hxJ9r3y91nVlWmaqZB5LnkzYrbCT51TQe2VWmiOOfucdcSV52Y2S+Bowj6TEv5biFo3AO41d3nlbNtrWRm+wF/BI5099x4vH9YRXlstQXmlLP+WiCH4GPhU6okUXyL5v36Z+TrbcARQCuC/pqTzewAd98Z04TxpSLvV1FBPp6ggDq3RBeg2qBC75f8RNFvsJLXTdHywirMIjWcmf2c4N6O14CHQo5THfwXmAAcDtxqZinF++bXdpFPEp4AnnD3yWHnKYuK8hhy9yWUc7d9pEiaBVwC7Iz0dUqIrEsCCt291vyi29P7VWLbzcAnAGY2E5hOMBrEc7HKF28q8n5FRvZ5D0gGjnb3rBhGi0sVeb+kVFsjz/UJPuUrUo+gIFf3AqkUZnYtcC/B/Qs/r4UNCBXm7tMjX06MjB51vZndUeJ+otrsaoLuPSdF6qsiZmZJka5AodONnuE6kuAX3GsEN2fkEfwgIvL1rSHliltmdlpk9JDiZhK8X21DiBT3zOwg4FOggKC/9PQ97CJSmgWR54wSyzOAeSqcpDKY2V8Ihrl9DjjL3XNDjhS3zKyVmV0SKcKL+47gRs+mIcSKV6cT1Aib+F+91ZfgnrS8eLmHSC3l4XobKFlgngdcF1m+qsoTxb8bgd3AocWWHU7QAjwjlERxLPKD5j2Cls0j3V3XlOytBcBy4DTgA/ihn/6JBCOwiOwTM/stwWg1DwDX6g+9PWpEMJII/HgElmOAdZGHBC4naAQt7gVgPsHNsXHxu1FFeYjcfSPBeKI/MLNDIuumhBIq/t0FvGVmowkmlugG3EHQl05jbv/UAwQ36P0K6GBmxSfDWeruq8OJJdWNu7uZ3Q08ZGabgUkEo2U0I5jARGSvmVlr4G8EjSsvAQeVuBFvSrx0MYgX7j7XzP4D3GtmKQQjIZ0BjAAurU3dX/ektBtfzWwXsDGe6i0V5VKtuPvbZnYqwZ3mIwhGr3kOuFmtKj8WacU8AUgEXixlk+sJRmIRiYq7PxKZnOS3BDfGfg8c6+6LQg0mNcGxBF0uegOl3YjXHNhQpYmqhwsJZqe8CWgNzEYTnlVbmtFTRERERCRkutFTRERERCRkKspFREREREKmolxEREREJGQqykVEREREQqaiXEREREQkZCrKRURqICsxyHO8iNdcIiJhU1EuIlLDRMbyH1XO+ilm9mEpyx81MzezO0pZN9vMXo5lLhGR2kxFuYhIzXMt0Lac9Z8QzJhY8nfAUcAm4OjiC82sCbAfMD7GuUREai0V5SIitc8EoD7Qs2iBmXUEugAPAIPMrFGx7Q8GjH0vykVEpAwqykVEahAzmwAcCpwY6YrSqZTNPgMKgCHFlh1NMI35Q5HXhxdbdwiwzN2zIudIN7MHzWytme0yswlmdkCxDBeb2QYzuz7yPM/Mvi4tl5l1MbM3zGy7mW0xs+fMrFllvBciItWJinIRkZrlKuA7YBJB0b265Abuvg2Yyo+L8qOA8e6+CfiWH3dhORj4CH64UfMt4FzgZuBsIAeYYGaZxfZpBFwC/Bz4I3BxyVxm1hL4HOgIXAhcEVn3gZml7OX3LyJSLSWFHUBERCqPu882s23ADnf/spxNJwCnwg+F9pHATZF1HxEU25hZKjAQeCSy7hjgCOBody8q1McBswiK70sj2yUCt7r7+0UnLJnLzK4B0iLH2hBZ9hWwgKDof3av3gQRkWpILeUiIjWYmSWVeBQNSfgJ0C1yE2c/oBmR1vDIcxcz6wAMAlKBjyPrDgd2AhOLjhlZ/gFBYV/c7D3EOxyYDGwpdqzlkf1KHktEpEZTS7mISM2WV+L1JcDTBN1GCoDBQC9gobsviWwzCdgFDCcYLWWWu6+JrGsK1AVyozjXuj1kawocVMp+AGtKWSYiUmOpKBcRqdkGlXi9GMDdd5jZlMj6wfyvlRx3321mnwNDgfb8eNSVrQTF9omVkG0r8B5waynrtlfC8UVEqg0V5SIiNU9B0RfuPqWc7T4h6C8+FHisxLqPgJMJxicvvu5z4DqCvuFzixaa2f0EwyaWd76CEq8/B04BZrj77shx0oDXgP8C88o5lohIjaI+5SIiNc8WoIeZHWZmdcrZ7hPgWKBe5OviPiLoWtIYmFhs+dvAN8C7ZnaRmR1uZg8B1wBzKpjrPoJRWt4zs1PN7ARgLMGNpFP39E2KiNQkKspFRGqe+whuzhwHHFDOdpMAB6a6++YS674DtkXWbS1a6O4FBIX8h8DfgXcJ+p5f4u6jK5LL3ZcRjIG+E3geeIng99JR7v79nr9NEZGaw9w97AwiIiIiIrWaWspFREREREKmolxEREREJGQqykVEREREQqaiXEREREQkZCrKRURERERCpqJcRERERCRkKspFREREREKmolxEREREJGQqykVEREREQvb/OK4muhZLccUAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Erzeuge x-werte\n",
"x = np.linspace(-4, 4, num=1000)\n",
"\n",
"# Plotte t-Verteilung\n",
"fig, ax = plt.subplots()\n",
"\n",
"ax.set_title(\"t-Verteilung, df = 5\")\n",
"ax.set_xlabel(\"t-Werte\")\n",
"ax.set_ylabel(\"Wahrscheinlichkeitsdichte\")\n",
"ax.plot(x, t.pdf(x, df=5))\n",
"for _t in [-4, -2, 0, 2, 4]:\n",
" ax.vlines(_t, ymin=-0.025, ymax=t.pdf(_t, df=5), linestyle=\"dashed\")"
]
},
{
"cell_type": "markdown",
"id": "4a7ba11e-8aec-46d8-920e-9d881a6861fb",
"metadata": {},
"source": [
"Eine weitere sehr nützliche Funktion ist die Funktion `t.cdf()`, die die Fläche unter der $t$-Kurve für ein beliebiges Intervall liefert. Berechnen wir die Fläche unter der Kurve für die Intervalle $j_i= \\ ]-\\infty \\ $,$ \\ -2]$ , $]-\\infty \\ $,$ \\ 0]$ , $]-\\infty \\ $,$ \\ 2]$ und $k_i=[-2 \\ $,$ \\ \\infty[$ , $[0 \\ $,$ \\ \\infty[$ , $[2 \\ $,$ \\ \\infty[$ für eine Zufallsvariable mit einer $t$-Verteilung mit $df=5$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d82065ff-9410-4f78-ab00-edf053633de4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wert für Fläche links von -2: 0.05096973941492914\n",
"Wert für Fläche links von 0: 0.5\n",
"Wert für Fläche links von 2: 0.9490302605850709\n"
]
}
],
"source": [
"x_cdf_left = []\n",
"# Berechne kumulitative Wahrscheinlichkeit links von Wert _t\n",
"for _t in [-2, 0, 2]:\n",
" res = t.cdf(_t, df=5)\n",
" print(f\"Wert für Fläche links von {_t}: {res}\")\n",
" x_cdf_left.append(res)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8c4cba9d-59af-45c5-bd3f-aaa2ef8a196c",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import t\n",
"import matplotlib.pyplot as plt\n",
"\n",
"df = 5\n",
"fig, ax = plt.subplots(figsize=(16, 8), ncols=3)\n",
"# axis 0\n",
"x = np.linspace(-3.2, 3.2, 1000)\n",
"for e, _t in enumerate([-2, 0, 2]):\n",
" ax[e].plot(x, t.pdf(x, df=df), color=\"C0\", linewidth=4)\n",
" ax[e].vlines(_t, ymin=0, ymax=t.pdf(_t, df=df))\n",
" ax[e].fill_between(x, t.pdf(x, df=df), where=x <= _t, color=\"r\", alpha=0.5)\n",
" ax[e].text(\n",
" -0.7,\n",
" 0.4,\n",
" s=r\"$P(X \\leq {t}) = \\int_{-\\infty}^{t}f(x)dx$\",\n",
" horizontalalignment=\"center\",\n",
" size=18,\n",
" )\n",
" ax[e].text(\n",
" 2,\n",
" 0.3,\n",
" s=f\"Fläche = {np.round(t.cdf(_t, df=df),3)}\",\n",
" horizontalalignment=\"center\",\n",
" size=14,\n",
" )\n",
" ax[e].set_title(f\"$t={_t}$\", size=18)\n",
"for _ax in ax:\n",
" _ax.set_ylim(-0.02, 0.45)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "85ac807b-f930-41ec-b7ad-f4037c35a1ea",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wert für Fläche rechts von -2: 0.9490302605850709\n",
"Wert für Fläche rechts von 0: 0.5\n",
"Wert für Fläche rechts von 2: 0.050969739414929105\n"
]
}
],
"source": [
"x_cdf_right = []\n",
"# Berechne kumulitative Wahrscheinlichkeit rechts von Wert _t\n",
"for _t in [-2, 0, 2]:\n",
" res = 1 - t.cdf(_t, df=5)\n",
" print(f\"Wert für Fläche rechts von {_t}: {res}\")\n",
" x_cdf_right.append(res)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "ff05efd5-2ecf-438c-92f5-162b3d4cf7f4",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import t\n",
"import matplotlib.pyplot as plt\n",
"\n",
"df = 5\n",
"fig, ax = plt.subplots(figsize=(16, 8), ncols=3)\n",
"# axis 0\n",
"x = np.linspace(-3.2, 3.2, 1000)\n",
"for e, _t in enumerate([-2, 0, 2]):\n",
" ax[e].plot(x, t.pdf(x, df=df), color=\"C0\", linewidth=4)\n",
" ax[e].vlines(_t, ymin=0, ymax=t.pdf(_t, df=df))\n",
" ax[e].fill_between(x, t.pdf(x, df=df), where=x >= _t, color=\"r\", alpha=0.5)\n",
"\n",
" ax[e].text(\n",
" -0.7,\n",
" 0.4,\n",
" s=r\"$P(X \\leq {t}) = \\int_{-\\infty}^{t}f(x)dx$\",\n",
" horizontalalignment=\"center\",\n",
" size=18,\n",
" )\n",
" ax[e].text(\n",
" 2,\n",
" 0.3,\n",
" s=f\"Fläche = {np.round(1-t.cdf(_t, df=df),3)}\",\n",
" horizontalalignment=\"center\",\n",
" size=14,\n",
" )\n",
"\n",
" ax[e].set_title(f\"$t={_t}$\", size=18)\n",
"for _ax in ax:\n",
" _ax.set_ylim(-0.02, 0.45)"
]
},
{
"cell_type": "markdown",
"id": "7dc94a50-b686-4b25-bcfd-817d63524ab5",
"metadata": {},
"source": [
"Die Funktion `t.ppf()` liefert die Quantilfunktion und ist damit die Umkehrfunktion von `t.cdf()`. Für die Intervalle $j_i= ]-\\infty \\ $,$ \\ -2]$ , $]-\\infty \\ $,$ \\ 0]$ , $]-\\infty \\ $,$ \\ 2]$ einer Zufallsvariablen, die einer $t$-Verteilung mit $df=5$ folgt, liefert die Funktion `t.ppf()`..."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b6134bea-90f7-4ef5-98f5-f521c97d2d41",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0.05096973941492914, 0.5, 0.9490302605850709]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x_cdf_left"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "bfec625c-76a4-45fa-aa89-4e29a884ebfc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.05: -2.0\n",
"0.5: 0.0\n",
"0.95: 2.0\n"
]
}
],
"source": [
"for x in x_cdf_left:\n",
" print(f\"{round(x,2)}: {round(t.ppf(x, df=5), 2)}\")"
]
},
{
"cell_type": "markdown",
"id": "9f85f574-bfb3-4f8a-84dd-0d6468a1ea21",
"metadata": {},
"source": [
"... und für die Intervalle $k_i=[-2 \\ $,$ \\ \\infty[$ , $[0 \\ $,$ \\ \\infty[$ , $[2 \\ $,$ \\ \\infty[$ einer Zufallsvariablen, die einer $t$-Verteilung mit $df=5$ folgt, liefert die Funktion `t.ppf`"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "692c0a2e-8679-4a5c-bc82-a1b070355209",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.95: 2.0\n",
"0.5: 0.0\n",
"0.05: -2.0\n"
]
}
],
"source": [
"for x in x_cdf_right:\n",
" print(f\"{round(x,2)}: {round(t.ppf(x, df=5), 2)}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}