{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Математические инструменты"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверка отрисовки графика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XohQsex38Q6Dj/WanqZB0YbDCpysPkp2bx1P9nfCOys5jwbcmLH/D+IXSijW0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bc141dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Plot test frame\")\n",
    "x = np.linspace(0, 2*math.pi)\n",
    "plt.plot(x, np.sin(x), label=\"sin(x)\")\n",
    "plt.plot(x, np.cos(x), label=\"cos(x)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Численное интегрирование"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Вариант 1: простой интеграл Римана\n",
    "Фиксированное количество точек. Интеграл всегда сходится, но точность результата зависит от функции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "def integrateR(func, a, b, numPoints = 400):\n",
    "    res = 0\n",
    "    points, step = np.linspace(a, b, numPoints, endpoint=True, retstep=True)\n",
    "    return np.sum(func(points))*step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Вариант 2: итеративный интеграл Симпсона \n",
    "Используется [итеративный численный интегратор из библиотеки SciPy](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.integrate.simps.html), \n",
    "в основе которого лежит [квадратичная формула Симпсона](http://mathworld.wolfram.com/SimpsonsRule.html). Первый аргумент - сама функция, второй и третий - границы интегрирования. \n",
    "Итеративная формула гарантирует точность интегрирования, но не гарантирует сходимости."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# from scipy.integrate import simps\n",
    "# def integrateS(func, a, b):\n",
    "    \n",
    "#     return simps(func( np.linspace(a,b, 5000, endpoint=True)), np.linspace(a,b, 5000, endpoint=True))\n",
    "# # integrateS = {UnivariateFunction func, Number a, Number b -> new SimpsonIntegrator().integrate(5000,func,a,b)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import quad\n",
    "\n",
    "def integrateQ(func, a, b):\n",
    "    return quad(func, a,b)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Интегратор по умолчанию\n",
    "В качестве интегратора по умолчанию выбираем интегратор Римана. Если захотим использовать другой, надо переопределить переменную `integrate,` например вот так:\n",
    "\n",
    "`integrate = integrateS`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "integrate = integrateR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверяем, что интегратор работает"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Итеративный интеграл:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateQ(np.sin,0, math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 100 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9998321638939927"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateR(np.sin,0,math.pi,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 400 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999896675538067"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateR(np.sin,0,math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 5000 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999999341763102"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateR(np.sin,0,math.pi,5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Свертка"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "[Сверткой](https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D1%91%D1%80%D1%82%D0%BA%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7) \n",
    "двух функций называется следующее интегральное преобразование:\n",
    "$$\n",
    "  h(x) = f(x) \\otimes g(x) = \\int {f(x-y) g(y) dy }\n",
    "$$\n",
    "Интегрирование ведется по всей области определения функций. Очевидно, что переменные под интегрированием можно менять местами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "convolute = lambda f, g, a, b: np.vectorize(lambda x: integrate(lambda y: f(x-y)*g(y), a, b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверяем работу свертки"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Проверяем работу свертки, взяв в качестве одной функции ступеньку, а в качестве другой Гауссиану. Параметры `wStep` и `sigma` можно менять по своему усмотрению для получения различного результата."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/+ctfAHj77be55ZZbghl+wHmT3DsD7pN6s5zHqhCRbkAKsLSa8zeKyBoRWZOTk+NrrErV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bc9e4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wStep = 2; # Ширина ступеньки\n",
    "sigma = 0.5;# Стандартное отклонение Гауссианы\n",
    "\n",
    "# ступенька\n",
    "f = lambda x: 1/wStep if (x >= -wStep/2 and x<= wStep/2) else 0.0 # нормировка на единицу\n",
    "f = np.vectorize(f)\n",
    "\n",
    "# Функция Гаусса\n",
    "g = lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-x*x/2/sigma/sigma)\n",
    "\n",
    "# Plot plot = new Plot(title: \"Convolution test plot\", showLegend: true)\n",
    "\n",
    "\n",
    "# автоматическое определение окна интегрирования и отрисовки\n",
    "wind = max(2*wStep, 4*sigma)\n",
    "x = np.linspace(-wind, wind, 300)\n",
    "plt.plot(x, f(x),  label=\"f(x)\");\n",
    "plt.plot(x, g(x),  label=\"g(x)\");\n",
    "plt.plot(x, convolute(f,g, -wind, wind)(x), label=\"convolution\");\n",
    "plt.title( \"Convolution test plot\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Интерполяция"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "При использовании численных методов часто нужно уметь не только вычислить функцию, но и сохранить ее значения в виде таблицы для дальнейших вычислений.\n",
    "В данном случае используется кубический сплайн-интерполятор из библиотеки commons-math. Сплайн-интерполяторы характерны тем, что выдают гладкую функцию, проходящую через все заданные точки. \n",
    "Легко видно, что для функций с большой степенью гладкости такой интерполятор будет выдавать хорошее приближение даже при сравнительно маленьком количестве узлов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import CubicSpline\n",
    "\n",
    "def interpolate(func, a, b, numPoints=300):\n",
    "    xs = np.linspace(a,b, numPoints, endpoint=True)\n",
    "    spline = CubicSpline(xs, func(xs), extrapolate=False)\n",
    "    \n",
    "    def my_spline(x):\n",
    "        if x<a:\n",
    "            return spline(a)\n",
    "        elif x>b:\n",
    "            return spline(b)\n",
    "        else:\n",
    "            return spline(x)\n",
    "        \n",
    "    return np.vectorize(my_spline)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### Проверка работы интерполятора"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mWh1HqSxTefRUTA44MmO81VE8ghZ3F7P4zcEEHbvBweZBBFYNsTqOUlnmnkbt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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bcb38128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Testing function interpolation (sin)\")\n",
    "x = np.linspace(0, math.pi, 300, endpoint=True)\n",
    "plt.plot(x, np.sin(x), label=\"original\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 10)(x), label=\"10 points\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 100)(x), label=\"100 points\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 200)(x), label=\"200 points\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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thhH3qMcXc6/ioGh2pl5jMzYxBDYZbEdiI0hKr7K4m7CMfTHiHu34smUcZS2o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\nG4ZhpCDm3A3DMFIQc+6GYRgpyP8AozCpQusBbt0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bcbb2668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Testing function interpolation (step)\")\n",
    "x = np.linspace(-1, 1, 300, endpoint=True)\n",
    "# ступенька\n",
    "f = lambda x: 1 if (x >= -0.5 and x<= 0.5) else 0.0 # нормировка на единицу\n",
    "f = np.vectorize(f)\n",
    "\n",
    "plt.plot(x, f(x), label=\"original\")\n",
    "plt.plot(x, interpolate(f, -1, 1, 10)(x), label=\"10 points\")\n",
    "plt.plot(x, interpolate(f, -1, 1, 100)(x), label=\"100 points\")\n",
    "plt.plot(x, interpolate(f, -1, 1, 200)(x), label=\"200 points\")\n",
    "plt.plot(x, interpolate(f, -1, 1, 300)(x), label=\"300 points\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Распределения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Равномерное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Равномерное распределение говорит о том, что величина может принимать любое значение в заданном интервале $(a,b)$ с равной вероятностью.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "  f(x) = 1/(b-a),  a < x < b\n",
    "$$\n",
    "\n",
    "Равномерное распределение с конечными пределами указывает на то, что величина лежит строго в заданном интервале, но ее точное значение в этом интервале неизвестно.\n",
    "В случае бесконечных пределов нормировка равномерного распределения расходится, но его все равно можно использовать.\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu = (b-a)/2\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = (b-a)^2/12\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform = lambda a,b: np.vectorize(lambda x: 1/(b-a) if (x>=a and x<=b) else 0.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация равномерного распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xp2zf6D72FfeF15YJqCUD0bSMZtyTMzMKORubMgpCYTZYPrjKfXB4kLIHdJ4y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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bcc12b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Uniform distribution\")\n",
    "x = np.linspace(-1,1, endpoint=True)\n",
    "plt.plot(x, uniform(-0.5, 0.5)(x), label=\"d = 1\")\n",
    "x = np.linspace(-1.5,1.5, endpoint=True)\n",
    "plt.plot(x, uniform(-1, 1)(x), label=\"d = 2\")\n",
    "x = np.linspace(-2,2, endpoint=True)\n",
    "plt.plot(x, uniform(-1.5, 1.5)(x), label=\"d = 3\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Биномиальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Биномиальное распределение описывает вероятность получить число \"успехов\" $k$ при проведении $n$ экспериментов при условии, что вероятность успеха в одном эксперименте равна $p$.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   p(k) = \\frac{n!}{k! (n-k!)} p^k (1-p)^{n-k}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu  = np\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = np(1-p)\n",
    "$\n",
    "\n",
    "Для вычислений используется [библиотечная функция](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.binom.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация биномиального распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I9adRHwxTH2x6GUInsOUzCNVBvyPatl2/IwBjjbuvlHIM1yT9cNjYk6K3r6UP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\nRJO+Ukq5yP8D8NwtZkrIINgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bce5e320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Binomial distribution (p = 0.5)\")\n",
    "p =0.5\n",
    "x = range(0,10)\n",
    "plt.plot(x, binom.pmf(x,10,p), label=\"n = 10\")\n",
    "x = range(0,50)\n",
    "plt.plot(x, binom.pmf(x,50,p), label=\"n = 50\")\n",
    "x = range(0,100)\n",
    "plt.plot(x, binom.pmf(x,100,p), label=\"n = 100\");\n",
    "x = range(0,100)\n",
    "plt.plot(x, binom.pmf(x,150,p), label=\"n = 150\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Распределение Пуассона"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Распределение Пуассона описывает вероятность насчитать количество событий $k$ при условии, что все события равновероятны, а сренее количество таких событий равно $\\lambda$. \n",
    "Это распределение - одно из самых распространенных в физике, поскольку описывает отклонение от среднего в процессе достаточно произвольного вида.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   p(k) = \\frac{\\lambda^k}{k!} e^{-\\lambda}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu  = \\lambda\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = \\lambda\n",
    "$\n",
    "\n",
    "Для вычислений используется [библиотечная функция](http://commons.apache.org/proper/commons-math/javadocs/api-3.5/org/apache/commons/math3/distribution/PoissonDistribution.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Пуассона"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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17l7tVF39GemkfxrGV9j0t/TDyOeFnwMwM2umyZFoXRUbG0t5eblO/BamlKK8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\nBQ32kO3eOVR5iHp3PRPSJ5g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2TB+y0+Fg2W9+QV1VFQvu+znJfcJzJmrDMTulz+wCEdLv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bca35da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Poisson distribution\")\n",
    "for i, mean in zip([15,25,50,70,100,120,150], [5,10,20,35,50,75,100]):\n",
    "    x = range(0,i)\n",
    "    plt.plot(x, poisson.pmf(x,i), '-', label=\"lambda = {:d}\".format(i))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Нормальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нормальное или Гауссово распределение - наиболее часто встречается в физике (и не только). Оно является предельным случаем распределение Пуассона при больших $\\lambda$, \n",
    "а также всегда всплывает при усреднеии случайных величин в силу *центральной предельной теоремы*.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   f(x, \\mu, \\sigma) = \\frac {1}{\\sqrt{2\\pi} \\sigma} e^{-\\frac{(x-\\mu)^2}{2 \\sigma^2}}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu \n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = \\sigma^2\n",
    "$\n",
    "\n",
    "Параметр $\\sigma$ называют стандартным отклонением и именно он в большинстве случаев используется для оценки погрешности эксперимента."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция Гаусса\n",
    "gauss = lambda mu, sigma: lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-(x-mu)*(x-mu)/2/sigma/sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Гаусса"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0xuh7IaVyUzKSoqizNVBcVU+/2J6RbdNWYAHwyUzflJEBNhu2Awcw+2B8zU94\nIvoWwL32WxrQVkDtq4ArI1lHz22XtmbkviLYUyt3hPZsBY6aubZkJ3R8pp+aatwAxsbGcvHFF/P1\n1193i+ibQsUrKZWb4rp7yC+p6Tmib7EgJhNh/fp5fWxXkXRrbq4WfR/jieh/AwwXkcFAAcbC7MXu\nHURkuFJqt/Pp6YDr8UrgFRF5BGMhdzjwtTcM704KCwtJTEzk0ksvJSYmpllytClTpnDDDTdQWlpK\nbGwsb775ZocyWraUWnnmzJnN+nlrpn/rrbcyZcoUzj777E6d379/f7Zv387IkSN5++23W1w36MhM\n3263U1ZWRnJyMjabjffee4/Zs2d3yraOkF9SQ1pCFKFeSKncFPewzWMzu1Z7N1CwWgowpaR4JdFa\nU1yx+ra8PPBClllN67Qr+kopu4gsAlYDocBzSqlsEbkX2KSUWgksEpHZgA0oxXDt4Oy3AsgB7MB1\nwRi5E4yplQFmzJjBjh07qKqqIi0tjWXLljFnzhy+//57zjzzzE6P+8ADDzB//nzS09MZN24cVVVV\nXbKzvr6eOXPmYLPZcDgczJ49m1//+tddGtMTfBGj7yI13pli+UitT8b3BzaLxSeuHYCwfv2Q8HAd\nq98dKKUC6ufYY49VTcnJyWl2LNCorKxUSills9nU/Pnz1VtvveVni1rntNNO87cJncabn4UJd69W\nt7/9vdfGa8q0v3ysbnxti8/G7252Tp2mCu+8y2fj750/X+Vdc63Pxu/pYEzC29VYvSPXSwRTauXV\nq1f72wS/U15jo7zW5pNwTRc9KcWyo6oaR1kZprRmwXdew5SZqTdodQM6NspL6NTKwUV+qe/CNV1k\nJEbx+e7DPhu/O3FF7vhykdWckUn1uvWohgafrBtoDILmnVXtRMhoej7e/Az4IqVyUzISozhQUdcj\nUizbLL4L13RhzshAWa3YDx702TU0QSL6ERERHDlyRAt/L0YpxZEjR4iI8E74408bsyK9Ml5LuL5Q\nLKXBv5jbLaKfqROvdQdB4d5JS0vDYrFQXNwzqxFpPCMiIoI0L4lOXkkNidFmYiNMXhmvJdxj9Yf1\ni2mnd2BjtRQQEhVFaHy8z67RmG0zL5foac02/Wu8RFCIvslkYvDgwf42Q9ODyDviu3BNF66Zfu6R\nap9epztwhWv6MqVE2IABiMlkxOprfEZQuHc0Gm/ji5TKTUmOcaVY7hnuHV+6dgAkNBRTerp27/gY\nLfqaXofd0UBBWS0ZPvTnw08ploM926ZSCmtBgU/DNV2YMzJ0BS0fo0Vf0+soKvddSuWm9IRYfUdp\nKaqmplty4pgzDdHXQRu+Q4vc4OVzAAAgAElEQVS+ptfhy5TKTXHN9INZxLojcseFKSMDVVuLXQdt\n+Awt+ppeR3fE6LvISIyi1ubgcJXV59fyFY2i7+UyiS3hyrapF3N9hxZ9Ta8jr6SGsBBhYJxvffrQ\nM4qkW13FU7rDp69j9X2OFn1NryOvpIa0hEifpFRuinusfrBis1gITUggJDra59cypaRAWJhezPUh\nWvQ1vY58H6ZUbkpagnE3Ecwz/e4I13QhYWGYUlN0kXQfokVf0+vojhh9FxGmUAb0iQhq0bcWWLol\nXNOFOTWtcR1B43206Gt6FeW1NspqfJtSuSnBHKuvHA5shUXdWsLQlJ6uRd+HeCT6IjJXRHaKyB4R\nuaWF9htFJEdEtonIJyKS6dbmEJEtzp+V3jReo+koLt96pg+KobdGMMfq2w8eBJsNU1p6+529hCkt\nFUdZGY6q4E9fEYi0K/oiEgo8DswDxgAXiciYJt2+AyYrpSYAbwAPubXVKqWynD+dr9Gn0XiB/G6M\n0XcRzCmWrY0x+t3o3nHeVbhy+Gu8iycz/SnAHqXUPqWUFXgVWODeQSm1Rinlmsp8Cehy9pqApDs3\nZrnISIpEKSgoC74cPLbGcM1udO+4RD8/v9uu2ZvwRPRTAfd33+I81hq/BD5wex4hIptE5EsRabGG\noIhc7eyzSadP1viSvJIaEqJM9PFhSuWmZCRGN1472LBZLCCCaeDAbrumS/St2q/vEzxJrdxSMHOL\ne8pF5FJgMnCS2+EMpVShiAwBPhWR75VSe48aTKmlwFKAyZMnB+9+dU3A052ROy4ygjhW31ZgMVIe\nm83dds3Q+HhCoqMb7zI03sWTmb4FcF/FSQMKm3YSkdnAbcCZSql613GlVKHz9z5gLTCpC/ZqNF0i\nrxtj9F0kx5iJNIWSeyT4RN9qKcCc2n3+fDCyk5rSdNimr/BE9L8BhovIYBExAwuBo6JwRGQS8DSG\n4B9yO54gIuHOx8nACUCOt4zXaDqC3dFAQWltt8/0gznFcnduzHLHlJamF3J9RLuir5SyA4uA1cB2\nYIVSKltE7hURVzTOw0AM8HqT0MzRwCYR2QqsAR5QSmnR1/iFovI67N2UUrkpwRi22WC1Yj90yC+i\nb05LxWopCOrspIGKR+USlVKrgFVNjt3p9nh2K+dtBMZ3xUCNxlvkd2N2zaZkJEaxce9hlFI+LTno\nTWwFBaBUt4ZrujClpqFqa3EcOUJYcnK3X78no3fkanoN/gjXdJGRGEmNNbhSLPsjXNOFKd0Ztqn9\n+l5Hi76m1/BTSuWIbr92hnMHcH5p8Lh4XD51/7h3XGGbOoLH22jR1/Qa8kpqSE2IJCy0+z/2wRi2\nabNYEJOJsH79uv3aJmfEkJ7pex8t+ppegz9i9F2kJRjXDaawTaulAFNKChLS/TIREhVFaFISVove\nletttOhreg3+FP1gTLHsr3BNF6a0VL1Bywdo0df0CvyRUrkpwRar72/RN6fpFMu+QIu+plfgz3BN\nF8EUq++oqsZRVuaXcE0XprQ0bEVFKLvdbzb0RLToa3oFrhl2Rjfm0W9KMKVYdkXu+CNc04UpLRUc\nDmwHDvrNhp6IFn1Nr8CfMfouMpOiUAospYGfYtlm8V+4povGvPp6MderaNHX9Ar8kVK5KelBFLYZ\nCKLfmFdf+/W9ihZ9Ta8g34+ROy5c1w+GxVyrpcAIm4yP95sNpgEDIDRU59X3Mlr0Nb2C3CM1ZCRF\n+9WG5BgzUebgSLHsitzxZ54gMZkwDRigwza9jBZ9TY/H7migoKyWjMRIv9oRTCmW/R2u6ULn1fc+\nWvQ1PZ6i8jocfkqp3JRgCNtUSmG1WDCnB4Lop2LVefW9ihZ9TY8nECJ3XLhm+oGcJ95eXIyqrcWU\nmelvUzCnpeEoPkxDbeBHPAULWvQ1PR6XDz3Tzz59MES/1uaguKq+/c5+wpaXB4A5w/+ib0ozKrXa\nCrRf31t4JPoiMldEdorIHhG5pYX2G0UkR0S2icgnIpLp1naFiOx2/lzhTeM1Gk/IK6nBFCoM6NP9\nKZWbEgzZNq25TtHPzPCzJTTuCNYRPN6jXdEXkVDgcWAeMAa4SETGNOn2HTBZKTUBeAN4yHluInAX\nMBWYAtwlIgneM1+jaZ/8khrSEqIIDfF/xSrXjuBAXsy15uVBWBimgQP9bYrbBi090/cWnsz0pwB7\nlFL7lFJW4FVggXsHpdQapZTrU/wl4FoBmgN8pJQqUUqVAh8Bc71jukbjGXklNQHhzwdIjY9EBPKO\nBK6P2pqXizk1FQnzqJqqTwlNTkYiInQEjxfx5K+aCrjvg7ZgzNxb45fAB22c2yyDk4hcDVwNkJHh\n/1tKTc8i90g1Wemd2GRUdQjWLYHKopbbM6bBlN9AqOfi6EqxnFtS3XF7uglbbh6mAPk/FBFMqak6\nr74X8eTT2tI9cYuhByJyKTAZOKkj5yqllgJLASZPnhy4YQ2aoKO8xkZFnb1j4ZpKwbbX4MNbwFoN\niUOb93FYYftKo9+Cx2HAeI+HD+SwTaUU1rw84iZN8rcpjZjT0rR7x4t4IvoWIN3teRpQ2LSTiMwG\nbgNOUkrVu507s8m5aztjqEbTGTocrlmWD+/dAHs+gvSpcOa/oO/IlvvmvAvv3wRLZ8IJf4ATF4Op\n/cXizMQo1u0u9vAVdC+O0lIaqqoCYhHXhSktjZrNm1FK+XWHcE/BE5/+N8BwERksImZgIbDSvYOI\nTAKeBs5USh1ya1oNnCYiCc4F3NOcxzSabiHP0zz6DQ3w9TPwxDTI3QjzHoKrPmxd8AHGLIDrvoLx\nF8D6JfD0DMj7ql2bMhKjOFhRH5Aplq25uQAB494BQ/QbqqpoKC/3tyk9gnZFXyllBxZhiPV2YIVS\nKltE7hWRM53dHgZigNdFZIuIrHSeWwLch/HF8Q1wr/OYRtMtuHznbebRrymBF+bDqpsg7Ti49guY\n+hvwpDZsVCKc/SRc+ibYauG5OfDRnYaLqBVctgSiiyeQYvRd/BS2qV083sCjFSil1CpgVZNjd7o9\nnt3Guc8Bz3XWQI2mK+SX1JAUbSYmvJWPusMGKy4HyybDN591CXTGhTBstvFlsfo22PAoRCXDCb9r\nsWu6W7bN4f1jO34tH2LNzYOQEL9WzGqKOd25QcuST+S4sX62Jvjxf0yWRuND2g3X/PBW2L8ezn4a\nJi7s2sXCY+GMR6Gu3Jjt9xsNw09t1i0zgFMsW/PyMA0cSIjZ7G9TGtF59b2LTsOg6dHktZVHf9O/\n4Ztn4Pjruy74LkTgrCdgwDh44xdQvKtZl8RoM9Hm0IAV/UBaxAUIjYkhNC5O78r1Elr0NT0Wm6OB\nwrI6Mlvy5+/fYPjwh82G2fd498LmaFj4Hwg1w6sXQW3pUc0iQnpiFHkBmFfflpsbUIu4Lkw6bNNr\naNHX9FgKy2pxNKjm7p2yPFhxGSQMhnOXQUio9y8enw4XvgylufDGL8FhP6o5EPPqO8rLcZSXB9Qi\nrgudV997aNHX9FhaDNesr4L/XGSI8EWvQqQPywFmTof5j8DeT+Dju45qCsQUy9Y8Y9droLl3AMzp\nadgKClANDf42JejRoq/psTQT/YYGeOcaOJQD5z8HycN8b8QxlxupGr54DLa80ng4MymKensDxZWB\nk2LZmmfE6JsD1L2jbDbshw6131nTJlr0NT2WvCM1mENDfkqp/NVTRuqEU+8zfPndxZy/wOCT4L+/\nh0M7gJ/CNnMDyMXjitE3pae307P7MaXqCB5voUVf02PJK6khLTGSkBCBikJYcz8MPw2mX9e9hoSG\nwXnPgSnKWDxWP5VuDKTFXGtuHmEDBhAS4f+6A03RefW9hxZ9TY/lqHDN1bdBg91Ir+CP/C3RyTD7\nLmNPwPdvkJrgTLEcQDN9a15eQLp2AEypqSCiI3i8gBZ9TY9EKUXeEafo710D2W/Bz26ExMH+M+qY\nKyDlGPjfbYTbq0iJiwyoVAzWvDxMGYHn2gEIMZsJ698fW75OsdxVtOhreiRlNTYq6+0Mig8zXCoJ\ng+GE3/vXqJBQOP1vRp7+NX8hPTEyYHz6jqpqHIcPB2S4pgtTWirWAu3e6Spa9DU9EpfbZEbxq3Bk\nD/x8iUdpj31O6jEw+Rfw9VKmRhYEjHvHlu9KtBaY7h0Ac1o6tjw90+8qWvQ1PZK8khrSpJihO56E\n0WfA8G6M1mmPWXdAZCILix/lcGUttVb/p1gOpGLorWEeMgT7oUM4qqr8bUpQo0Vf0yPJK6nhzrAX\nEQmFuQ/425yjiUyA0+5jYMU2zgtdR36p/2f71sZwzcAV/fChQwCw7t3rZ0uCGy36mh5J1P6POS10\nM3LSHyEuzd/mNGfiRVT1P45bwv5DQWGzQnTdjjUvl9DkZEJjov1tSquEDzXKVtbv3ednS4IbLfqa\nnoetlp9b/k5+aDpMu9bf1rSMCI55S4ijmgGbHvK3NdhyAzdc04UpLQ0xmajfu8ffpgQ1Hom+iMwV\nkZ0iskdEbmmh/UQR+VZE7CJyXpM2h7OaVmNFLY3Gp3z+D/o7DvBuyo0QFjh54ZvSJ3Miy5nHqII3\noeBbv9oSyDH6LiQsDPPgwVj1TL9LtCv6IhIKPA7MA8YAF4nImCbd8oArgVdoTq1SKsv5c2YL7RqN\n96g6hNr4L953TMWafoK/rWkTEWFlwhVUhsTBx3f7zY6G2lrsBw8G9CKuC/PQIdRrn36X8GSmPwXY\no5Tap5SyAq8CC9w7KKX2K6W2AToFnsa/rH8E7HUssV/QdsWsAKFvUjIvmc6FHz+DfWv9YoPVueEp\nEPPoNyV86DBsFgsNdXX+NiVo8UT0UwH34FiL85inRIjIJhH5UkTOaqmDiFzt7LOpuLi4A0NrNG6U\n5cGmZRwYci4/qoFkJgXuoqSLjKQonqw+CdUnDT65t82C6r4iEIuht0b40CGgFNYff/S3KUGLJ6Lf\nUqKSjnwyM5RSk4GLgX+IyNBmgym1VCk1WSk1uW/fvh0YWqNxY+2DgLAx7VcArZdJDCDSE6OosodR\nMfVGKNgMO97vdhsaY/QDNAWDO2ZXBM8e7eLpLJ6IvgVw/zSkAR7HmCmlCp2/9wFrgUkdsE+j8Yzi\nXbD1FTjuV+ys7YM5LIR+seH+tqpdXF9MOwecAUnD4dM/Q0P3btay5uURGh9PaFxct163M5gHDYKQ\nEOr3adHvLJ6I/jfAcBEZLCJmYCHgURSOiCSISLjzcTJwApDTWWM1mlZZ82cjdfGMG9lXXEVmYpSR\nUjnAGeSs37vvSB2cchsUb4fvX+9WG6x5uZiCYBEXjMRr5owMrHqm32naFX2llB1YBKwGtgMrlFLZ\nInKviJwJICLHiYgFOB94WkSynaePBjaJyFZgDfCAUkqLvsa7FH4HOe8aefKjk9lxoJKRA2L9bZVH\npCdEEWkKZceBShi9AAZMgDV/Abu122yw5eUHhT/fhXnoUOr36bDNzhLmSSel1CpgVZNjd7o9/gbD\n7dP0vI3A+C7aqNG0zSf3GakNpl9HZZ0NS2ktF00JkplriDByQCw7DlRASAjMuguWnwvfvgBTfu3z\n6zdYrdiKiogLgsgdF+FDh1L12Wcomw0xmfxtTtChd+Rqgpv9nxuFx392I0TEsetgJQAj+wfHTB9g\n1IBYdh6oNIqkD5sFGcfDuofBWu3za9ssBdDQEBSLuC7Chw4Bu70xX5CmY2jR1wQvSsHH90DswMZZ\n8fYiQ/RHDQwu0S+tsXGost6o6jX7Lqg6CF897fNru4qhB0OMvgvzUKOgvY7g6RweuXc0moBk12qw\nfA3z/w6mSAB2HqgkNjyM1PjIDg+nlOJQzSG2l2xn+5Ht5JTksLt0N7X22hb7J0YkMjpxNKOTRjM6\ncTSjEkcRY47p8HVHDewDwI4DlfTvEwEZ02D4HNjwDyP3fmR8h8f0lMYY/czg8emHDzGqn1l1BE+n\n0KKvCU4aGuDT+4yKWJMuazy840AFIwfEIh7Wwa2x1fBR7kes3r+a7CPZlNSVACAIg+IGMSF5An3C\n+zQ7TynFgZoDfFn0Jf/d99/G45l9Msnqm8WZQ89k8oDJhEj7N9OjnIvOO4oqOGmEc5/KKbfD0zNg\n47+M/Ps+wpqbR0hMDKEJCT67hrcJiYrClJKiZ/qdRIu+JjjZvhIO/gBnPw2hxmKeUoodBypZkJXS\n5qlKKbYUb+GdPe/w4Y8fUmOvIS0mjRmpMxidNJoxSWMYmTCSKJNnm7uKa4ob7w62l2znk7xPeHfv\nu6TGpLJg6AIWDFtASkzrNsVHmRnQJ8KI4HExcAKMPRu+esrIFBqd5JEtHcWVaM3TL8lAQUfwdB4t\n+prgo8EBa/9qbGYaf37j4cLyOirr7Iwa0HxmDlBeX87ru17n3T3vsr9iP5FhkcwZNIezhp3FMf2O\n6bTw9Y3qS9+ovpyYdiIAtfZaPsn7hHf2vMOTW5/kya1PMmXgFM4Zdg5zBs0hNCS02RijBsYeLfoA\nJ90C2e/Axn/Cqfd0yrb2sOblEjGmaf7EwCd86FBqvv4a5XAgoc3fT03raNHXBB/Zb0PxDjh3mVFs\n3MmOogrgJ3eJizp7Hcu3L2fZ98uotFVyTL9j+MW4XzBn0ByPZ/MdITIskvlD5jN/yHwKqwp5d++7\nvLvnXW5efzNLty3lhmNv4MS0E4/6khk5IJYNew5jczRgCnW6hPqNgvHnwddLYfoiiPFuihJls2Er\nKKTP3HleHbc7MA8dgqqvx1ZYiDk9eCKPAgEdvaMJLhoc8NmD0He04f5wwzVTHuEUfUeDg7d3v838\nt+fzj2//waT+k3jzzDd5Yd4LnD38bJ8IflNSYlK4ZuI1rDpnFY/MfAS7srPo00VctfoqthVva+w3\nekAfbA7FvuImYZon3Qz2Otj4qNdts+bng90eVIu4LsIbI3h0QZWOokVfE1z88CYc3gUzbzlqlg+G\n6KclRBIbHsY6yzrO++953LnxTvpG9uW5Oc/x+KzHGZEwwi9mh0gIp2aeytsL3ub2qbfzY/mPXLLq\nEm5ceyO5FbmNIaY7DlQcfWLycBh/AXz9LFQe9KpNddnGxvmIscHo3nHWy9V+/Q6jRV8TPDjssPYB\n6D8ORjevx7OjqIIhA+xc+8m1XPfJdVgdVpactIRXTn+F4wYc5weDm2MKMXHhqAtZdc4qrpl4DZ8X\nfM5Z75zFhwXPExbiaO7XBzjpj+CwGiGcXqTuh2wkPLyx9mwwERoXR2jfZB3B0wm0T18TPHy/Akr2\nwoUvGykL3Kiz2cm1rqdE3iPkgIM/HvdHFo5ciCk0MLfpR5uiuTbrWi4YeQF/3/x3lv3wDH2GpvHd\ngauBUUd3ThoKEy+Cb5bB8b+DPgO9YkNdTg7ho0YiYcEpA+FDhupsm51Az/Q1wYHDZvjyB0yAUfOP\najpSe4TrPv4D4QNfY0BUJm+c+QaXjbksYAXfneTIZO7/2f08evKjEFZBNvfw7PfPYm+wH93xxJtA\nOeDzR7xyXdXQQF1ODpFjx3plPH8QPnQo1j17jfQVGo/Roq8JDra+CqX74eQ/GakKnHyc+zHnrDyH\nzcUbqDs4j0dmPE1mn+BbmDwl4xQuTXsMW+UYHv32Ua748Ar2l+//qUPiYMi6GDY/D+UFXb6eNTeX\nhupqIoJY9M1Dh9BQXY390CF/mxJUaNHXBD52K6x7CFImwYi5gLGT9rbPb+OGtTfQP6o/p8U/gFSc\nzNDklmP0g4FJaanUFVzM1aPuYH/5fs7773ms2Lnip5nsjJuMfEPr/9bla9VlGxnOg1n0dQRP59Ci\nrwl8tiw36t+efBuIkFeRx6UfXMp/9/6X30z4DctPX05RcTzD+8UQFhq8H2ljf4EQ1zCFtxe8zeT+\nk7nvy/u4fcPt1NnrICETjrkMvn3ReD+6QF12NmI2B+UirovwYYbt1r06gqcjBO9/iKZ3YK+HdUsg\n7TgYNps1eWtY+N5CDtUc4snZT7Jo0iJMISZ2HKhsdSdusDCgTwRxkSa2F1XSL6ofj896nGsmXsPK\nvSu57IPLyK/Mhxn/Z7i31j3cpWvVZWcTPnJkUOejD01KIiQujvq9ejG3I3gk+iIyV0R2isgeEbml\nhfYTReRbEbGLyHlN2q4Qkd3Onyu8Zbiml7DpOaiw4Jh5C//87l/8bs3vSO+TzmvzX+OE1BMAOFJV\nT3FlPaODKJ1yS4iIM7e+EasfGhLKtVnX8visxymoKmDhewtZV7kPjr0KvlsOhzvn1nAt4gZjfL47\nImIs5mrR7xDtir6IhAKPA/OAMcBFItL005IHXAm80uTcROAuYCowBbhLRIInnZ/Gv9RXwrqHKR38\nM67Zt4Jnvn+Gc4afw4vzXiQ1JrWx205nbHuwlEhsC1dBlYaGnyJSTkw7kdfmv8bA6IEs+mQRTyT3\npSEswqgL3AlseXk0VFUFtT/fRfjQIXqm30E8melPAfYopfYppazAq8AC9w5Kqf1KqW1AQ5Nz5wAf\nKaVKlFKlwEfAXC/YrekNfPEEO20VLIyoZvPBzdw9/W7uOf4ewkPDj+rm2tAU7O4dMHLrV1sdFJQd\nncM/PTadl37+EmcMPYMnt7/I9cPGUZ3zDhRu6fA1ap07cYM5XNOFeehQHKWl2EtK/G1K0OCJ6KcC\n+W7PLc5jnuDRuSJytYhsEpFNxcXFHg6t6dFUH2bd5ie5PC0Vu4Ty4rwXOXfEuS123XGgguQYM31j\nw1tsDyZcyeK2F1U0a4sMi+TPJ/yZ26bexob6Q1yWmkLRxx3PtV+Xk4OYTIQPG9Zle/2NayFau3g8\nxxPRbynfrKe7ITw6Vym1VCk1WSk1uW9f72YS1AQfSimWr17E9UkxZPYZxCunv8LY5NZnpTsOVPYI\n1w7AiP6uHDwtpGPA8GMvHLWQJ2Y9QVF4BBfZ9vL91hc7dI267BxjEdds7rK9/sYl+vU6gsdjPBF9\nC+CeuzQNKPRw/K6cq+mF2Bvs3L/uVh6ozGamOZnn5/+H/tH9W+3vaFDsOhj8kTsuosPDyEyKalyn\naI3jU4/n5XkvESEhXPXdw6z+cbVH4yulnIu4we/aAQgbOBCJitJ+/Q7gieh/AwwXkcEiYgYWAis9\nHH81cJqIJDgXcE9zHtNomlFpreS6T67jtf3vc1VFNX+f90K76Y9zj1RTZ2tolkM/mBk1IJbtTbNt\ntsDQ5LG8Mm4RY+rruGndTSzdtrTdlAS2/HwaKiqCsnBKS4gI4UOGaPdOB2hX9JVSdmARhlhvB1Yo\npbJF5F4RORNARI4TEQtwPvC0iGQ7zy0B7sP44vgGuNd5TKM5ioKqAi5bdRlfF33FPYdLuHHERYQk\ntJ9OoSct4roYOaAP+w9XU2dztNs38dhf8Yy1D6fbQvnXd//i9g23Y3PYWu3/UzrlnjHTBx3B01E8\nitNXSq1SSo1QSg1VSt3vPHanUmql8/E3Sqk0pVS0UipJKTXW7dznlFLDnD//9s3L0AQz2UeyueT9\nSzhUe4inwzI5p17gZzd6dO6OA5WECAzvH+NjK7uP0QNiaVCw+2BV+51DwwifdSd/tfzItf1/xsq9\nK/ntx7+lwtrynUJddjaYTISPGO5lq/2Heegw7AcP4qho/+5Io3fkavzMOss6rvrwKsJDw3n5mFuY\nsmstnPA7jwuB7yiqYHByNBGmnlMnddRA467FExcPAKPPRFImcc329fxl+j18e/BbrvjgCg5UH2jW\ntTY7m4jhwwnpAYu4LiInTACgZvNmP1sSHGjR1/iN13e9zvWfXs+gPoN4ed5LDPliKUQlw7RrPR6j\nJ6RfaEpGYhQRphB2FLW9mNuICMy+G8rzOePIAZ489UkOVB/gkvcvYUfJjsZuxiLu9h7l2gGInJSF\nmM3UfPmVv00JCrToa7qdBtXAo98+yr1f3MsJKSfw/Nzn6Vu4FfavhxMXQ7hnrprqejt5JTU9ahEX\nIDREGNk/lp0HO+CuGDITBp8E65cwLX4kL8x7ARHhig+uYEPBBgBsBQU0lJf3ONEPCQ8n8phjqP5K\ni74naNHXdCtWh5Vb19/Ks98/y7nDz+Wfp/yTKAmFD/4IScNg8lUej7XzYM9Jv9CUkQNiPZ/puzjt\nz1BbCmv+woiEESz/+XLSYtO47pPreHv329T90PMWcV1ET5tK/Y4d2EtL/W1KwKNFX9NtlNeX85uP\nfsOqH1fxu0m/467pdxEWEgZfPAYl+2DeQxDm+a5aVyz76IE9y70DRjTSkWorxZX1np80cAJM/iV8\n8ywUbaN/dH9emPsCUwZM4c6Nd7Lh0xchLIzwkf4pDu9LoqZOBaDmq6/9bEngo0Vf0y0UVBVw+QeX\ns6V4C3/52V/49YRfIyJQlm+kTh41H4bN6tCYO4oqiAkPIzU+0kdW+49RA107czsYkXLKbRCZAKsW\ng1LEmGN4fPbjnDXsLMq3fUfJwGgcoS1tlA9uIseNIyQqipqvtYunPbToa3xO9mEjJLO4tpilpy7l\njKFn/NT4v9uNalBz/9rhcbcfqGRE/xhCQnqeiLkWpzvs4olMMBZ187+Eba8BYAoxcc/0exhzOJzv\nEivaDOkMVsRkIvK4yVTrxdx20aKv8Smf5X/GVauNkMyX5r3EcQOO+6lx7xrIeccoDBKf0aFx62wO\ntlnKmJAW72WLA4PEaDNpCZF89WMn9jJmXQqpx8L/7oA6Q9zthUWYquoYf8JZfHvICOksrOpZGVGi\np07Dum8ftoO6Zm5baNHX+IzXdrzG79b8jsFxg1l++nKGxruV5rNbjcXbhMFw/PUdHnvj3sPU2Ro4\nZVQ/L1ocWJwyqh8b9hz2aGfuUYSEwM+XQHUxrH0A+Gkn7pSZC3lq9lMcrD7IJasuIedIjrfN9hvR\n05x+fe3iaRMt+hqv42hw8LdNf+PPX/2ZGakz+Pecf5McmXx0p6+egsO7YN6DYIro8DU+3n6IaHMo\nU4ckesnqwGPW6P7U2hx8sfdIx09OPQaOvcJ4nw9tN0Q/LIzwkSOZOnAqL857EVOIiSs/vJLP8j/z\nvvF+IHzUKELi4qj+8r8HE4EAACAASURBVEt/mxLQaNHXeJUaWw1/WPsHns9+ngtHXsg/Tv5H86Rp\nFUXw2YMwYi6MmNPhayil+HT7IWYM70t4WM/ZiduUqYMTiTKH8smOg50b4JQ7IaIPrFpMXU4O4cOG\nERJuREcNSxjG8p8vZ3DcYK7/9HpeyH6h3WRtgY6EhBA95Ti9SasdtOhrvEZRVRGXfXAZ6y3r+dPU\nP3H7tNuNkMymfHQHOGydWrwFyC6s4EBFHbNG91zXDkCEKZQZw5P5dPuhzglydBKccgfqx/XUbfu2\nWU3cvlF9eX7u88zOnM2STUu4+4u720zWFgxETZ2GraAAq8Xib1MCFi36Gq+wtXgrC99fSFFVEU/M\neoKLRl3Ucsf9n8P3r8MJv4fEIZ261qc7DiECJ/dgf76LWaP6U1hex/aORvG4OPZK7DHjcFTUEDFi\naLPmyLBIlpy0hKsnXM1bu9/i6o+upqyurItW+49Gv7528bSKFn1Nl3l/3/v84sNfEG2K5uWfv8zx\nqce33LGuHN65BhIGwc9u6PT1Ptl+kKz0eJJjgr88Ynu4vtg+2d5JF09IKDUDFgIQWfZJy10khOsn\nXc9fZ/yVbcXbuHjVxewrD85KVOahQwlNTtahm22gRV/TaRpUA//67l/csv4Wxvcdzys/f4Uh8W3M\n3lcthvICOOcZMLddHKU1DlXWsdVSzqxeMMsH6BsbzsT0eD7Z0fkwxIqvdhIWF0nEkffghzdb7Td/\nyHyWzVlGta2aS9+/tDFnTzAhIkRPnUr1V18G/RqFr9Cir+kU5fXlXPvJtSzdtpRzhp/DM6c+Q3xE\nGzHz2143NguddDOkT+n0ddc4xW/W6NZLKPY0Zo/qx1ZLWcdSMjhxlJdT/dk6+iw4D0mfDO/dYOyC\nboWsfln85/T/MDBmINd8fA1Pb32aBtXQFfO7nahpU3EUH8a6LzjvVnyNR6IvInNFZKeI7BGRW1po\nDxeR15ztX4nIIOfxQSJSKyJbnD9Pedd8jT/YfmQ7F753IV8VfcUd0+7g7ul3Ywo1tX5CaS68fyOk\nTzM2YnWBT7YfIiUuosdl1myLU0b3QylYs7Pjs/3Kjz5C2Wz0OeNMOPcZaHDA2781frdCSkwKL817\niXmD5/HYlsf4/ae/D6odvNHTpgHorJut0K7oi0go8DgwDxgDXCQiTQts/hIoVUoNA/4OPOjWtlcp\nleX8+a2X7Nb4iXf2vMNlH1yGvcHOC3Nf4IKRFxg5dFrDYYe3rjYen7MUQluI5vGQOpuD9bsPM2t0\n/7av2cMYM7APA+MiOuXXL3/vfcyZmUSMG2ssnP/8Ycj9HDb8o83zokxRPDDjAW6dciufF3zOwvcW\nsrNkZ2dfQrdiSksjLGWgDt1sBU9m+lOAPUqpfUopK/AqsKBJnwXAC87HbwCzpDf9V/YCrA4r935x\nL3dsuIOsvlmsOGMFE/pOaP/Ezx8x8sCc/jfwoOZtW3y57wi1Ngen9PBQzaaICKeM6sf63Yept3u+\nO9d28BA1X31Fn/nzf/qSnHgRjD0b1vwFCtquNCUiXDz6Yv6/vXOPr6K6Fv93nXPyJA8SEsIjPML7\n5YOXghW0QBUBsQoWahUqV7291lvbXm5btVh/2t/vV+vFtrYVHwjioy1YQHlpRLFAtQrIU0AISRDC\nKw+Sk4QkJzln1v1jJhjCOclJcpJAMt/PZzKTmT0za/bZs2bvtfdea+nkpVR4K7h7w92szVzblEdp\nEUy7/hjKPvsMNS4v01RLEIzS7w7UNALmWPv8prECqbuB6nh3aSKyS0Q2i8g4fzcQkQdEZIeI7MjL\ny2vQA9g0P8dLjjP33bm8dfgt5g2bxwvfeoHEyCBmwh7fbroBuOJOuPI7TZbjw4O5RIU5GdsnuFCK\nbYlJg1Moq/TxaVbwvniK390AqsRNnfr1ThGY9juISYGV94On/ji8V3c2P/JDk4by6D8f5def/poK\nb0VjHqPF6DDmWnxuN55Dl0frpCUJRun7q7HX7hYPlOYU0FNVhwM/Bf4iIhc5P1fVl1R1lKqOSk5O\nDkIkm5ZAVXn7yNvMXDOTr4q/4nc3/o6fjPyJ/wlXtfGUwKr7IK676QcmBLJs+jKX6/sntal4uMEy\ntm8nIsMcbGqAiad43Xoihwwhok/ahQeiEuD2F80YBumPBHWtpKgkXr7pZeYOmcvyQ8uZvW72BaEY\nLzWq/evbQzcvJhilnwP0qPF/KlDbPd/5NCLiAuKBs6rqUdUCAFX9HMgE2l4EhzaI2+Nm/ub5LPh4\nAUM6DWHl9JVM6jUpuJMNA9b8CIqOmXb8qKZ7wvzydAknisrbzVDN2kSGObm+XxIfBDk715OdTcUX\nXxA3bZr/BGnj4Pofw87XYM/yoGQIc4Qxf/R8Xpz0Iu5KN3etv4tXv3j1khzdE9alC+G9e9uTtPwQ\njNLfDvQXkTQRCQdmA2tqpVkDzLW2ZwKbVFVFJNnqCEZE+gD9AXsc1SXOtlPbuGPNHWw6tomHRzzM\n4psW0zWma/AX2LgA9q+CCQug19iQyLTJGqrZlr1q1sfEwSmcKCrn8Jn6TTLF6zeACHFTbgmc6MZH\nodf18M4PIXNT0HJc1/06Vk1fxbju41j4+UIe2PgAZ841cvJYMxI95lrKtm9Hqy5v1xKhpl6lb9no\nHwLSgYPAClXdLyJPish0K9krQCcROYJpxqke1jke2CsiezA7eH+gqo1wEG7TElT6Knl2x7Pc9/59\nRLuieWPqG9x3xX04HQ0wp3zyRzP84TUPNGnWbW0+OHiGK1Pj6RzXcI+cbYXqD94H9Zh4VJXideuI\nHj2asC5dAid0hcPsNyFpACy/B07uDlqWhMgEfv/N3/PE2CfYm7eXO9bcQfrR9KDPbwk6jBmDUVZG\n+d69rS3KJUVQ4/RVdYOqDlDVvqr6f619j6vqGmu7QlXvVNV+qnqNqmZZ+1eq6lBVvUpVR6jqpd/1\n307Zfno7M9bMYOn+pdw54E6WT1vO0E4NDKC9d4UZCWvIbTD5N2anYQjIL/Ww+3gREwe1nwlZ/kiJ\ni+SK7vHnWz2BqNh/gMqjR4mbNrXOdIBpert7pWnnf3OmaecPEhFhxoAZrJi2gh6xPZi/eT4Pb3qY\n0+dOB32N5qTDN76BIy6OgiVLW1uUSwp7Rm47p7CikMf++Rjz0ufhNby8OOlFFoxdcLE75Po48qHp\nV6f3OLj9JWhI66AePvoyF1XavFfNYJgwqDM7jxVSUBp4dm7x+vUQFkbcTTcFd9G4rnD3KjC88Pod\nUNqwEXS943vz+pTX+cnIn/DJyU+47e3beOPAG/jqmADWEjhjY0mcO4fSDz+k3AoiY2Mr/XZL9cic\n6W9PZ0PWBu6/4n5W37Y6sLO0uji5C1bMgeRBprmgEUFR6mLTl7mkxEUwtNtFA7/aHZMGp6AK/zjk\nXzGrz0fx+vXEjBuHs2MDOtCTB8Bdb0HJabPGH8RQzpqEOcKYN2weq29bzfCU4Ty9/Wnu2nAX+wta\nV9kmzpmDIy6O/D/9uVXluJSwlX475EjhEealz2PBxwtIi0/jrVvf4kcjfkSkqxHK+mwWvHknRCXC\n9/4OkfEhlbXU42XL4TwmDGpfs3ADMbRbHJ1jI3j3C/8mlLIdn+PNzSU+GNNObXqMhjtfhdP7YMU9\nZkjLBpIam8qiiYt45oZnyC3L5a71d/H0tqdxe9wNlycEOGNj6XTv9yn96CPK933RKjJcathKvx1x\n+txpFny8gBlrZ3Co8BC/GvsrXp38Kv0S+jXugmcOwLLbTD8u96wyzQQh5vcbD1NW5WPW6B71J24H\nOBzC7Gt68sHBM37DKBavW4dERxPzzW827gYDJ8P058zRPCvmNLjGD6atf3Lvybzz7Xe4c8CdvHnw\nTaasmsLSL5a2yqSuhHvuwRkfT/6f/tTi974UsZV+O8DtcbNwx0KmrprK+qz13DP4HjbcvoGZA2bi\nkEYWgcPp8Mq3wOcxFX5S/9AKDRw8VczST44ye3RPru7R9LH+bYUHb+xLj8Qofvn2Piq9X4+RNyor\nKX7/fWInTcQRFdX4Gwy/25xQl5EOS24251s0grjwOH455pe8detbXJl8Jc9+/izTVk9jdcbqFrX3\nO2NiSLz3Xko3b7ZH8mAr/TZNubecxfsWc8vKW1i2fxm3pN3C+tvXM3/0/LrdINeFKnz8HPxlFnTq\nC/d/BN2Gh1ZwwDCUx1bvo2NUGD+fPDDk17+ciQxz8uT0YWTmnePlrV+Ptjm3dSuG20381EaYdmpz\nzf2mua7oOLw8AY41fmbrwMSBLJq0iCU3L6FzdGce/+RxZqyZwaZjm1rM533C3Xfj7NiRPLu2byv9\ntsjZirMs2r2IySsn84edf2BkykhWTl/Jr6//dcMmWdXG64F3HjInXw25De59D+Jru2EKDct3HGfn\nsSIenTKYjtHhzXKPy5lvDurMLcO68NyHGRw/W4avtJTc3z6DKyWFDtc1ojPeH/0mwn0fQEQsLJsG\nu//apMuN7jKaN6e8ye9u/B0+9fHwRw/znXXfYW3mWqqM5p1A5YzpQOK8eZzbspXy3cHPR2iLyKUW\nXWbUqFG6Y8eO1hbjsiTbnc3rB15nTeYaPD4PN6TewLxh8xiRMqLpFy/NMzv3jv0LbviFGQzF0Tx1\nhoJSDxMWbmZQl1j+9sAYuwM3AKfc5UxauJlreifw1L7llKSn02vZq0SPHh3aG5WdhbfmQvYWM7bx\nxF81eUiu1/CyNnMty/YvI9OdSUp0Ct8b/D1mDphJbHjzxEowzp3jyKRvETl0KD0Xv9ws92hNRORz\nVR1Vbzpb6V/eGGrw+ZnPee3Aa/zj+D8Id4Rza99bmTNkTt2hCxvC4XRY/19wLg++/TwMmxGa6wZg\n/lt7eGf3Cd59eBz9OrefYCmNYfHWLHb/cTE/3Lua5J/+lKQH7m+eG/mq4N2fwY4l0OebpqvsThcH\nWm8ohhp8fOJjlu1fxmenPyPaFc2MATP47sDv0iMu9J33BYsXk/s/C+n1178QPTz0ZsnWxFb6bZxj\nxcdYm7WWtZlrOVF6goSIBGYPms2sgbPoFBUi18MFmZD+KBx+z5yqf/uL0D0ErYY6+CyrgFkvfcqD\nN/blZ5MHNeu92gKlu/eQfdf32N9tEFPX/oXYqGY2he1YAu8/bnbgX/efZiS08A4hufTBgoO8duA1\n3st+D696GdF5BNP7Tuem3jeFrPZvlJWZtf1Bg+i55JWQXPNSwVb6bZDiymLSj6azNnMtu3J3IQhj\nuo5her/pTOo5qXHj7P1ReQ62LjT96DjDTVPOtT8wfbU0I5Veg6nPbaW8ysfGn9xAVHj7c6HcEHxu\nN9l3zMBT5WX2qAeZNWEYv5xWO6hdM1ByGjb+Cvb+zXSdfdNTMPSOkLndOHPuDGuz1rImcw3Z7mwi\nnBFM6DGBW/veythuY4Nz7V0HBa8sIfeZZ+i5bBkdrm18vOZLDVvptxGOlxxnS84WtuZsZdvpbVQZ\nVfSJ78P0vtOZ2mcqXTrU4VCroajC/tWm/5ziE3DlbPjW/4HYEN6jDhb9I5On3/uSJd8fxYR27men\nPlSVnB8+ROnWrfR+43WezHSwYsdx1v3n9Qzu2kIzl499Chvmm5O5eo+DW56GlAb6a6oDVWV/wX7e\nOfIO7x59F7fHTUJEAtd3v57xPcbzjW7faFQLwCgvJ2vqNHxFRXRb+D/ENnZOwyWGrfQvU6p8VezJ\n28OWnC1sydlCpjsTgN5xvRmfOp4paVMY0mlIaDs3z+XD7r/A56/C2UzocoU5TrvnmNDdox62ZZ9l\n7pJtjB+QxIv31Ftu2z3VtdWURx8lcc49FJVVMnHhZrp2jOSVuaNJaSlvpIbPLDebnoLyQuhzI4z8\nPgycGtKWYZWvii05W9h4bCP/PPFP3B43LnExImUE41PHM677ONLi04J+L6rOnCHnwR9SceAAnefP\nJ3HevZf9gAFb6V8muD1u9uTtYeeZnezK3cX+gv14fB5c4mJkl5HckHoD41PH0yuuafFlL0IVjv4T\nPl8KB9eCrxJ6joWR98IVM0PqMK0uSj1efvvel7z2r6/okRjFin8fS9f4JkwsageUbd/OV9+/l9iJ\nE+n+h9+fV1bp+0/zo7/uItzlYMHUIdw5KrXlFFnZWdj+CuxcBu7j0CEZrv4ejJxrBmQPIV7Dy778\nfWw+vpnNOZs5UnQEgMTIRK5KvorhnYczvPNwhnQaQrgz8IfHKC/n5C8eoSQ9nfg77qDLE7/CEX75\nDg+2lf4lhqpSUFHA4cLDZBRmcLjwMAcKDpwvsC5xMbjTYK7ufDUjO4/k2q7XEhMeE1ohqsrh+DZz\n6N2Bt6HgiOkr56q7zJez8+DQ3q8eNh/O49FV+zjpLuf71/Xmv28eSHR40+y1bZnKo0fJX7QI99p1\nhPVIJe3vf8cZe6F5Izv/HD//+162HT3LuP5J/L/br6BHYgM9pjYFw2e6cNix1BwAoD5IuwEGTIa0\n8dB5SMiH+p4sPcknJz9hV+4udufu5liJOYM43BHOsKRhDEocRP+E/gxIGEC/jv0u8CCrhkH+n/5M\n/vPPEzVyJKl/fA5XYhDxny9BbKXfSpRVlXGi9AQ5JTkcLzlOTmkOWUVZZBRlcLbi6/gxSVFJDEwc\nyPDk4YxIGcGwpGFEuUJcw/VWwqndkLUZsjebCt/nAXGappvh98DQb0NYy9asi8oqeWrdQVbuzKFv\ncgd+O/NKRva6PF+0lqDy2DHyn1+Ee+1aJCyMhNmz6fTA/QGVk2Eob247xm82HESBn908kDlje+Nw\ntLD5ovgk7HoD9vzNNBsCRHcy7f9p482PQae+IesAria/PJ/dubvNj0DebjIKMyj3lp8/3iO2B/07\n9qd3fG9SY1NJjUkl5V8ZVD75LK6kJLo9/RuiRoxAmmkeSnMRUqUvIpOBPwBOYLGq/qbW8QjgNWAk\nUADMUtWj1rFHgH8DfMCPVLXO8DqXotJXVcq8Zbg9bgo9hRSUF5BXlkdeeR755fnklZnrE6UnKKi4\n0AlWTFgMveN6MyBxAP079qd/grkkRoZIyalChdt8qfIzIO8Q5B82l7NZpo90MO30aTeYL1vPsRDZ\nsm6K80rMQCi7jhWyYkcOhWWV/McNfXloQr92Gei8PtTnozI7m4IlS3G/8w7icpEwexad7rsPV3Jy\nUNc4UVTOo6v2sflwHlf36Mgtw7owvGcCV3SPb/mRUUXH4ehWs5WZtRlKrDDb4TGm36akgeY6eaA5\nPLhjr5C56DbU4ETpifMt7IzCDDKKMsgpyblgJvCAU8J/rzSIL/FRHhtO/lU9Kb9mCK5rR5KY3IOk\nqCTiI+KJj4gnwhkREtlCSciUvhXj9jDwLcwA6NuB76rqgRppHgSuVNUfiMhs4HZVnSUiQ4C/AtcA\n3YAPgAGqGtDbUmOVvqEGhRWFVBlVXy++KryGlyqjCo/Pg8fnocJbcX7b4/NQ7i2nrKqMc1XnKPPW\nWFeew13pxu1xU+wpxqtev/eNj4gnOSqZpKgkusd0P19zqF7HR8T7t6uqmgrZ6zHt6V6PWQv3VoK3\nAipLwVPy9VJZChXF5gSp0lwoPQPncs3tmp4LHS7Thpo0wFy6XmXWrDqEaOy+H1SVskofJRVeiiuq\nKKmoorjcS3b+OXZZij6n0KxpuRzCiF4JPD5tCMO6h9YN8+WCGgZaUYFRXm4upaVUHv0KT+YRKjOz\n8GRlUZmdjXo8SHg4HWfNotP99xHWueFBZFSVVTtP8NymDL4qKAPA6RAGdYlleM+OXJXakS7xkcRG\nhhEX6TLXUS4iXM34UVA1KyTZWyD3IOQfMissxScuTBcRDzGdISYFYpLNdXQn0y1EeIy5joiBiDhz\nroAzwuw8vmAdEbB/ymf4yCvPM1vkJTnklOZw5kwWsTsOk7r3DAMOnyOmAnwCh1LhYA+hMEZwd4CK\nmAiMjjFIYkfC4xPpEBFDtCua6DBz6RDWgWhXNJGuSCKcEUQ4I4h0RhLuDCfSFUmYI4xwZzhhjjBz\ncZrrCGcE8RGNey9CqfTHAk+o6s3W/48AqOr/r5Em3UrzLxFxAaeBZKxYudVpa6YLdL/GKv3sL7eT\ncd+cBp9XjUNBMJ0RifW/w/rfoWYTp3qfE3Cq4rTOqcbcvjA/a+6TWuvGYODEJw58OGssDrwSRhUu\nvLjQpjSXta5/leriUr1fFYw6ypDLIUSGOYkMcxIV5iAizBnq1nzzEujRaj7z+UxRa2WAoWAYqGFY\nax94fRgVFWh5uZ8LmoR170543z5E9O1HRN8+dBg3nrCU0EQMyy/1sOd4EbuOFbH7uLmUevxXZsJd\nDiJcDlwOwelw4HSAy+HA4QCHCILpQlng/EtQva8h1EwdpWX0ME7Q05dDsuaRoEUkGEUkaiEJWkSi\nUUgHyhr83AaCDycGjvPviyEODBwoguLAQFDE2meihlB6Vig7JchJITxAdG8FfE7wOcDrBK+19jnA\nsB5QxSpK1loDZFN+spPvvt04v//BKv1ges26A8dr/J8DXBsojap6RcQNdLL2f1rr3Is8dInIA8AD\nAD179gxCpIuJju6IMz6ihuK2CiYgCg7EUuJSQ6l/va9hCD5Me1X1//C1aje3v34T1CpQWGtFLMVs\nFTKpLnTV2w584rQUvOv8tiHOr68btKRNQC5YmXkqpgn2/DYQ5hTCHA5cTgdhTsHlMNfVyv6yJ5Ai\nk5pJ5MKdTqdpE3Y4wOlAxAEuJ47IKBxRUTiio5CoKBxR0Tiiownv2YPwtLSmuUSuh6SYCCYOTmHi\nYHMOhGEo2QXnOHuu8nzrrKSiiuIKL8XlVXi8Bj5D8ani81lrQzHU/PgrnPeSqef/BI9edEIMSme+\nYjhfBTjHoV4ijbKLlgijHJdW4dIqwrQSl1ae/9+BgUNNdS9qmGpffQgGolrjrTRwqOmq2qyYKRIH\n9FZElUrDQCp85lLutdY+HB4v+BSHAeGGEm4oGIphGBiAgZqLms9sWFl14TaoKB3jm7/1G4zS91fi\na/9agdIEcy6q+hLwEpg1/SBkuoiUnv1JWd++vefZ2DQEh0PomxxD3+C6CGzaCMF0T+cANT0fpQIn\nA6WxzDvxwNkgz7WxsbGxaSGCUfrbgf4ikiYi4cBsYE2tNGuAudb2TGCTmu2+NcBsEYkQkTSgP7At\nNKLb2NjY2DSUes07lo3+ISAdsw9ziaruF5EngR2qugZ4BXhdRI5g1vBnW+fuF5EVwAHAC/ywrpE7\nNjY2NjbNiz05y8bGxqYNEOzonctrypmNjY2NTZOwlb6NjY1NO8JW+jY2NjbtCFvp29jY2LQjLrmO\nXBHJg4AT8oIhCcgPkTihxJarYdhyNQxbrobRFuXqpar1TrW75JR+UxGRHcH0YLc0tlwNw5arYdhy\nNYz2LJdt3rGxsbFpR9hK38bGxqYd0RaV/kutLUAAbLkahi1Xw7DlahjtVq42Z9O3sbGxsQlMW6zp\n29jY2NgEwFb6NjY2Nu2Iy1Lpi8idIrJfRAwRGVXr2CMickREDonIzQHOTxORz0QkQ0SWWy6jQy3j\nchHZbS1HRcRvhBfr2D4rXbN7mhORJ0TkRA3ZpgRIN9nKwyMi8osWkOsZEflSRPaKyGoR6RggXYvk\nV33Pb7kLX24d/0xEejeXLDXu2UNEPhKRg1b5f9hPmhtFxF3j9328ueWy7lvn7yImz1n5tVdERrSA\nTANr5MNuESkWkR/XStMi+SUiS0QkV0S+qLEvUUQ2Wnpoo4gkBDh3rpUmQ0Tm+kvTIFT1sluAwcBA\n4B/AqBr7hwB7gAggDcgEnH7OXwHMtrZfAP6jmeVdCDwe4NhRIKkF8+4JYH49aZxW3vUBwq08HdLM\nct0EuKztp4GnWyu/gnl+4EHgBWt7NrC8BX67rsAIazsWOOxHrhuBdS1VnoL9XYApwLuY0fTGAJ+1\nsHxOzNjdvVojv4DxwAjgixr7fgv8wtr+hb8yDyQCWdY6wdpOaIosl2VNX1UPquohP4duA/6mqh5V\nzQaOANfUTCBmMNMJwN+tXcuAbzeXrNb9vgP8tbnu0QxcAxxR1SxVrQT+hpm3zYaqvq+q1VG6P8WM\nstZaBPP8t2GWHTDL0kRpaFTwBqKqp1R1p7VdAhzET8zpS5TbgNfU5FOgo4h0bcH7TwQyVbUps/0b\njapuwYw1UpOaZSiQHroZ2KiqZ1W1ENgITG6KLJel0q8Df0Hca78UnYCiGgrGb7D2EDIOOKOqGQGO\nK/C+iHxuBYhvCR6ymthLAjQpg8nH5mQeZq3QHy2RX8E8//k0VllyY5atFsEyJw0HPvNzeKyI7BGR\nd0VkaAuJVN/v0tplajaBK16tkV8AKap6CswPOtDZT5qQ51swgdFbBRH5AOji59BjqvpOoNP87As2\niHuDCVLG71J3Lf8bqnpSRDoDG0XkS6tW0GjqkgtYBDyF+cxPYZqe5tW+hJ9zmzy2N5j8EpHHMKOs\nvRngMiHPL3+i+tnXbOWooYhIDLAS+LGqFtc6vBPThFFq9de8jRmmtLmp73dpzfwKB6YDj/g53Fr5\nFSwhz7dLVumr6qRGnBZMIPZ8zKaly6qhNTpYe30yihkk/g5gZB3XOGmtc0VkNaZpoUlKLNi8E5GX\ngXV+DjVLQPsg8msuMA2YqJZB0881Qp5ffgjm+avT5Fi/czwXN99DjoiEYSr8N1V1Ve3jNT8CqrpB\nRJ4XkSRVbVbnYkH8Ls1SpoLkFmCnqp6pfaC18svijIh0VdVTlqkr10+aHMx+h2pSMfsyG01bM+/U\nG4jdUiYfYQZwBzOge6CWQ1OZBHypqjn+DopIBxGJrd7G7Mz8wl/aUFHLjnp7gPttB/qLOcopHLNp\nvKaZ5ZoM/ByYrqplAdK0VH4F8/xrMMsOmGVpU6APVaiw+gxeAQ6q6rMB0nSp7lsQkWsw3/GCZpYr\nmN9lDTDHGsUzBnBXmzZagICt7dbIrxrULEOB9FA6cJOIJFim2JusfY2nuXutm2PBVFY5gAc4A6TX\nOPYY5siLQ8AtUr7cnwAAAP9JREFUNfZvALpZ230wPwZHgLeAiGaS81XgB7X2dQM21JBjj7XsxzRz\nNHfevQ7sA/Zaha5rbbms/6dgjg7JbCG5jmDaLndbywu15WrJ/PL3/MCTmB8lgEir7ByxylKfFsij\n6zGb9ntr5NMU4AfV5Qx4yMqbPZgd4te1gFx+f5dacgnwZys/91Fj1F0zyxaNqcTja+xr8fzC/Oic\nAqos3fVvmH1AHwIZ1jrRSjsKWFzj3HlWOTsC3NtUWWw3DDY2NjbtiLZm3rGxsbGxqQNb6dvY2Ni0\nI2ylb2NjY9OOsJW+jY2NTTvCVvo2NjY27Qhb6dvY2Ni0I2ylb2NjY9OO+F+TB8g2bFgs7wAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bcef46d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Gaussian (Normal) distribution\")\n",
    "x = np.linspace(-10,10)\n",
    "plt.plot(x, gauss(0,1)(x), label=\"sigma = 1\")\n",
    "plt.plot(x, gauss(0,2)(x), label=\"sigma = 2\")\n",
    "plt.plot(x, gauss(0,3)(x), label=\"sigma = 3\")\n",
    "plt.plot(x, gauss(5,1)(x), label=\"sigma = 1, mu = 5\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Распределение Коши"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Распределение Коши (или Лорнца или Брейта-Вигнера) описывает резонансные процессы в физике.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   f(x, \\mu, \\gamma) = \\frac {1}{\\pi} \\frac{\\gamma}{ (x-\\mu)^2 + \\gamma^2}\n",
    "$$\n",
    "\n",
    "*Среднее значение:*  не определено\n",
    "\n",
    "*Дисперсия:*  распеделение Коши имеет бесконечную дисперсию (интеграл расходится)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "cauchy = lambda mu,gamma : lambda x : 1/math.pi * gamma/ ((x-mu)*(x-mu)+gamma*gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Коши"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CV5SOyS+tdcskLvy5wzeQVvAY8/ajje+CxgXPaG5K160baLWqp+8BziT9JCC/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\nJ9QPH3zeUVFjxqBLSFDLN5uhkr7iNVJ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9Wq68D+o6q/r+QwMJvvHkfl49Psq1HXX8zcfW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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bdf4cb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Cauchy distribution\")\n",
    "x = np.linspace(-10,10)\n",
    "plt.plot(x, cauchy(0,1)(x), label=\"gamma = 1\")\n",
    "plt.plot(x, cauchy(0,2)(x), label=\"gamma = 2\")\n",
    "plt.plot(x, cauchy(0,3)(x), label=\"gamma = 3\")\n",
    "plt.plot(x, cauchy(5,1)(x), label=\"gamma = 1, mu = 5\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Сравнение распределений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r1103GQ6st4Ob+Ref3frOTnX4aM42Xv9lM13uq5x9OIWYYTD/Tfj9FRj6o3tB\nuqRWrVrEx8ejI//mLiQkhFq1al14Rh9RfH6ZqtT7cvFOMo1hSJeo7AWZGfa5myrNoPlAV2K7WCGB\n/jzQqwH/nLqWOVsO0rORxyi3gWXsqKQ/PwXb50J0d/cCdUFgYCDR0Tk0DFHFll5SU8VCanom4xfv\noneTqtSpXDZ74ZqJkBRn+0vzK3679G0xtalZoQyv/7Lp3MtH7YdCWDVby1GqmCt+v05VKv2wag9J\nKWkM6xqVvSAr0z4kWa0VNLnOldgKKijAj4d7N2BV/FFmbTiQvfB0LWfnPFvLUaoY04SjfJ4xhk8X\n7KBR1TAuq+/1bM2G723tpvtj9kn9Ympgu1rUrVyW12duPnfMnPZDnFrOy+4Ep1Qh0YSjfN7SHYdZ\nt+cYQy+Lzn5T3RiY+7ptmda0eHfjHujvxyNXNmTD3mP8vG6fV2EZ6PYI7Jxvx/dRqpjShKN83qcL\ntlO+TCADvEfyjPsV9q2Gro+An3/Oby5GbmxdkwZVwnhj5mYyvWs57Qbb53Lmv+lOcEoVAk04yqcl\nHDnJjHX7ub1jbcoEeSWVea/bMWRa3eZOcIXM30945MqGbDlwnB9X78leGBRqe0/YNN12TqpUMaQJ\nR/m0zxfuxBjD3Z3rZi/YtcheYrrsIQgIcie4S+DaFtVpUq0cb87aQkZmVvbCjqMgoAzMfzvnNyvl\n4zThKJ91Mi2TCUt3cXWzatSq6NUUeu7rULayvdRUgvj5CX+5qhHbD6YwZUVC9sJQZ33XTISj8e4E\nqFQB5CvhiEgfEdkkInEi8lQO5T1EZLmIZIjIzV5lQ0Rki/NvSEEDVyXfdysTOHIi/dym0PvWwJYZ\n0OlP9lJTCXN1s6q0rFmet2dvId27ltPlAdtYYuF77gSnVAHkOeGIiD/wLtAXaAbcISLNvGbbBQwF\nxnu9txLwL6AT0BH4l4hUvPiwVUlne4XeQdPq4XSMrpS9cP5bEBQGHUe6E9wlJiI8elUjdh86yTex\nXjWZinWhxU2w7FMdFVQVO/mp4XQE4owx24wxacAEoJ/nDMaYHcaY1YDXaRnXADONMYeMMYeBmUCf\nAsStSriF25LYtD+ZYV2jsjeFPrYH1k2BdkOgTMk9Z7m8cSTt6lTgf7O3cCojM3th1z9DegosHZ3z\nm5XyUflJODWB3R6v451phfpeERklIrEiEqud9pVen87fQaXQIG5sXSN7wZKPwGRBp3vdCayIiAiP\nXd2YPUdTmbBkd/bCai2gwZWw+ANIP+lOgEpdhPwknJwe485rv+F5fq8x5iNjTIwxJiYyMjKnWVQJ\nt/vQCWZu2M8dHWsTEujRFDp8n1iNAAAgAElEQVQtBWLHQpPr7aWlEu6y+pXpFF2J//0Wx8k0r1rO\nZQ/DiYOwZpI7wSl1EfKTcOKB2h6vawF7cpm3MN+rSpnPFu7AT4S7O0dlL1g5HlKP2BvnpcDpWk5i\n8im+WLQze2F0D6jSHBa9bxsRKFUM5CfhLAUaiki0iAQBtwPf5/G9M4CrRaSi01jgameaUtmknMpg\nwtLd9G1RjWrlPQaWysqyB9ca7aB2J/cCLGIdoyvRvWEE7/+xlZRTGWcLRKDzfXBgHezQTj1V8ZDn\nhGOMyQAexCaKDcBEY8w6EXleRG4EEJEOIhIP3AJ8KCLrnPceAl7AJq2lwPPONKWymbwigeTUjHOb\nQm/5BQ5ttbWbYtxJ58V49KpGHEpJ49MFO7IXtLzFPou06H1X4lIqv/I1AJsxZjow3WvaMx5/L8Ve\nLsvpvWOAMRcRoyoljDF8On87rWqVp10drxZoi9613dg065fzm0uwtnUq0qtJFT6as427u9QlPCTQ\nFgSWgfbD7PAMh7ZBpXruBqrUBWhPA8pnzN1ykK2JKQy9zKsp9L41sH0OdLwH/APdC9BFj17ViKMn\n0xkzb3v2gg4jbceliz9yJzCl8kETjvIZny7YQURYMNe1qp69YNEHEFjWjn5ZSrWoWZ4+zasxeu52\njpxIO1sQXh2aD4AVX0DqMfcCVCoPNOEon7D9YAqzNx5gUKc6BAd4NIU+cQjWToJWt5boBz3z4i9X\nNSL5VAbjFni1WOv0J0hLhpVfuhOYUnmkCUf5hHELdhDoLwzqVCd7waoJkJEKMSPcCcyHNK5Wjl5N\nqvD5oh2kpns8l1OrvW25t/gDO+S2Uj5KE45yXXJqOpOWxXNdy+pUCfdoCm0MxI6BWh2geiv3AvQh\nI7pFc/B4Gt+v8nqMrdO9cHgHxM1yJS6l8kITjnLdt8viOX4qg2Fdo7MX7JgLSVsgZrg7gfmgy+pX\npkm1coyZtx3j+cBnkxsgrCos/cS94JS6AE04ylVZWYZxC3fStk4FWteukL0wdgyEVLA3xRVgex8Y\n2b0eG/clMz8u6WxBQJBtVLFlJhzanuv7lXKTJhzlqj82J7L9YMq5tZvk/bDhB2gzyD5vos64oXV1\nIsKC+WTetuwF7YaA+MGyse4EptQFaMJRrhq7YAdVw4Pp26Ja9oIVn0NWBsQMcycwHxYc4M+QLnX5\nfVMicQeSzxaUrwlNroXln0N6qnsBKpULTTjKNdsSjzNncyJ3dapLoL/HrpiVaQcYi+4BEQ1di8+X\nDepcl+AAP0bP25G9oMNIOHkI1k91JS6lzkcTjnLNlBUJ+Anc1qF29oK4WXB0tzYWOI9KoUEMbFeL\nycvjSTp+6mxBdE+o3BCWfOxecErlQhOOcoUxhikrEujaICJ7U2iwjQXCqtpxb1SuRnSL4lRGFl8u\n3nV2ooit5STEwp4V7gWnVA404ShXLNt5mPjDJxnQ1mvg1yO7YPMMaHt3qe03La8aVCnH5Y0j+Wzh\nzuzDULe+3XYFpENQKx+jCUe5YsqKBMoE+nNNc6/GAsvG2bP0UtxvWn6M7FaPg8dP8f1KjwdBy1Sw\nQxesmQQnD7sXnFJeNOGoIpeWkcWPq/dydfOqhAZ7jJCRkQbLP4OGV0OF2rkvQJ3RtYF9EHS094Og\nHUZCxklY+ZV7wSnlRROOKnK/bzrA0ZPp9Pe+nLZpGqQc0MYC+SAiDO8WzcZ9ySzY6vEgaPVWtn+1\npZ/Y0VKV8gGacFSRm7oygcqhQXRvEJG9IHYMlK8DDa50J7Biql+bGvZB0LleD4J2GGlHSd3+uytx\nKeVNE44qUsdS05m14QA3tK5BgOezNwe32EHW2g+xA4qpPAsO8OfuznX5zftB0Gb97BDUsTrQrvIN\nmnBUkfp5zT7SMrLOvZwWOxb8AqDdYHcCK+bu6lyHoAA/xszfcXZiQLDtGmjjdDi2J9f3KlVUNOGo\nIjVlRQLREaG0rlX+7MT0k3bwsKY3QFgV94IrxiqHBXNTu5p8uyyeQykeI4LGDAOTabu7UcplmnBU\nkdlz5CSLtifRv01NRORswbopkHpEGwsU0PCu0fZB0EUeI4JWqgf1e9uugjIzXItNKdCEo4rQ96v2\nYAz0b1sje8HS0bY7lqju7gRWQjSsWo6ejSL5bJHXg6AxwyF5D2z+2b3glCKfCUdE+ojIJhGJE5Gn\ncigPFpGvnfLFIhLlTA8UkXEiskZENojI3wonfFWcTF2RQLs6FahbOfTsxL2rbDcsMcPtA5+qQEZ2\njyYx+RQ/rNp7dmKjPlCuhjYeUK7Lc8IREX/gXaAv0Ay4Q0Saec02AjhsjGkAvAH8x5l+CxBsjGkJ\ntAfuPZ2MVOmwYe8xNu5LPrcrm9ixEBACbe5wJ7ASpluDCBpXLccnc7edfRDUP8C2/tv6Kxzadv4F\nKHUJ5aeG0xGIM8ZsM8akAROAfl7z9APGOX9PAnqLvVhvgFARCQDKAGnAsQJFroqVqSsSCPATrmvl\ncTkt9RisnggtboIyFd0LrgQREUY4D4Iu9HwQtN1gEH97L0cpl+Qn4dQEdnu8jnem5TiPMSYDOApU\nxiafFGAvsAt4zRhz6CJjVsVMZpbhu5V7uLxxJJVCg84WrJkI6SnaWKCQ3dimBhFhQXwyz2Oo6fAa\ndnC2FV9Axqnc36zUJZSfhJPTBXaTx3k6AplADSAaeExE6uX4ISKjRCRWRGITExPzEZ7yVYu3JbHv\nWGr2Z2+MgaVjoForqNneveBKoJBAf+7qXJfZGw8Qd+D42YKY4XAiCdZ/515wqlTLT8KJBzx7VKwF\neD9NdmYe5/JZeeAQcCfwszEm3RhzAJgPxOT0IcaYj4wxMcaYmMjIyHyEp3zVlBUJhAUHcGXTqmcn\n7l4CB9ZpY4FL5K7OdQkK8GPsfI9aTvTltpm0Nh5QLslPwlkKNBSRaBEJAm4Hvvea53tgiPP3zcBs\nY+9c7gJ6iRUKdAY2Fix0VRykpmfy09p99G1RjZBAjy5rYsdAUDnbjb4qdBFhwQxoU5Nvl3s8COrn\nZxP8roWwf527AapSKc8Jx7kn8yAwA9gATDTGrBOR50XkRme20UBlEYkDHgVON51+FwgD1mIT11hj\nzOpCWgflw2Zt2M/xUxnZW6edOGQf9mx9GwSHuRdcCTeiezSp6VmMX+zxIGibQeAfrLUc5YqAC89y\nljFmOjDda9ozHn+nYptAe7/veE7TVck3dUUC1cJD6FSv8tmJK7+EzFPaWOASa1S1HN0bRjBu4U7u\n6VGP4AB/KFsJmg+AVV/Dlc9pwldFSnsaUJfMoZQ0ft+USL82NfD3c+7TZGXZs+vanaFqc3cDLAVG\ndq9HYvIpfvR8EDRmOKQlw5pv3AtMlUqacNQlM231HjKyTPbWadv/sA8fau2mSPRoGEHDKmHZRwSt\n3RGqtoDY0ba1oFJFRBOOumSmrEigSbVyNK0efnZi7BgoU8mO1aIuudMPgq7fe4yF25JOT7QJf98a\nSFjmboCqVNGEoy6JnUkpLN91JHvt5the2DgN2g6CwBD3gitl+retSeXQIEbP9Wgi3epWCAqzHacq\nVUQ04ahLYuqKPYjAja09urJZ8bkdm6X9MPcCK4VOPwj668YDbEt0HgQNLmeTzrrJttWgUkVAE44q\ndMYYpq5MoHN0ZWpUKGMnZmbYfrzqXQGV67saX2l0V+e6BPn7Ze/uJmY4ZKTCqq/cC0yVKppwVKFb\nFX+U7QdTsj97s+UXOJagjQVcElkumIHtajJpWTyJyU5fatVaQq2O9r6aNh5QRUATjip0U1ckEBTg\nR5+W1c5OjB0N5apD477uBVbKjepRj/TMrOzd3XQYAUlxsH2Oe4GpUkMTjipU6ZlZ/LBqD1c1rUp4\nSKCdeGg7xP1qu8j3D3Q3wFKsXmQYfZpX4/NFO0lOTbcTm/W3Q0PEauMBdelpwlGFat6WgySlpGVv\nnbZ8nG2K226we4EpAO7rWZ/k1Ay+WrLLTggMsd3dbJwGyfvcDU6VeJpwVKGasiKBCmUD6dnI6ek7\n4xQs/xwa9YXytdwNTtG6dgUuq1+Z0fO2cyoj006MGQ5ZGfZ7UuoS0oSjCs3xUxn8sn4f17WsTlCA\ns2tt+AFOHNTGAj7kvp712X/sFFNXJNgJletDvcttK8KsTBcjUyWdJhxVaGas3Udqelb21mmxY6BC\nXajfy73AVDbdG0bQvEY4H87ZRlaW0zotZgQci4fNM9wNTpVomnBUoZm6MoFaFcvQvm5FO+HABtg5\nH2KG2bFYlE8QEe7rWZ9tiSn8sn6/ndi4L4RV02EL1CWlRwFVKA4cS2V+3EEGtK2JnB7BM3YM+AdB\n27vdDU6do2+LatSpVJb3/9hqO/X0D4T2QyBuFhze4XZ4qoTShKMKxfer9pBloF8b53LaqeOw8is7\n9kpohLvBqXME+PtxT496rNp9hEXbnK5t2g2xrQmXfepqbKrk0oSjCsXUlQm0qlWeBlWcAb3WTLRj\nrnQY6W5gKle3tK9FRFgQH/yx1U4oX9O2Jlz+uW1dqFQh04SjCmzL/mTWJhyj/+najTG2F+JqLaFW\nB3eDU7kKCfRnWNdo/ticyLo9R+3EDsNtq8INP7gbnCqRNOGoApu6MgF/P+GG0z1D714M+9fa2s3p\n+znKJ93VqS6hQf58+Mc2O6FeL6gYpY0H1CWhCUcVSFaWYeqKPXRrEEFkuWA7celoCA6Hlre4G5y6\noPJlAxnUuS4/rt7DrqQTtjVh+2G2deGBDW6Hp0oYTTiqQGJ3HibhyMmzz94cT4T1U6H1HRAU6m5w\nKk+Gd43G30/4eK5Ty2l7l21dqLUcVcg04agC+SZ2N6FB/lzVrKqdsOJzyEyzvRCrYqFa+RAGtK3J\nxNjdHDx+yrYqbNYPVk2AtBS3w1MliCYcddGOn8pg2pq9XN+qBqHBAbZblNixENUdIhu7HZ7Kh1E9\n6pOWmcW4BTvshJgRcOoYrJnkalyqZMlXwhGRPiKySUTiROSpHMqDReRrp3yxiER5lLUSkYUisk5E\n1oiIDmpfzE1bvYcTaZnc2qG2nRA3C47u0qbQxVCDKmFc3awqny3cyfFTGVCnM1RpZoct0MHZVCHJ\nc8IREX/gXaAv0Ay4Q0Saec02AjhsjGkAvAH8x3lvAPAFcJ8xpjlwOZBe4OiVqybGxlM/MpR2dSrY\nCUs/sd2jNLnO3cDURbmvZ32OnkxnwpJdtnVhzHDYuwr2LHc7NFVC5KeG0xGIM8ZsM8akAROAfl7z\n9APGOX9PAnqL7efkamC1MWYVgDEmyRij3dIWY3EHklm28zC3dahtu7I5tB22zIT2Q3WQtWKqbZ2K\ndK5XiU/mbictIwta3QaBobBUGw+owpGfhFMT2O3xOt6ZluM8xpgM4ChQGWgEGBGZISLLReSJ3D5E\nREaJSKyIxCYmJuYjPFWUvomNJ8BPGNDWGeNm2VgQP9sflyq27utZn33HUvluZQKEhEOrW2Dtt3Dy\nsNuhqRIgPwknpyf4vC/u5jZPANANGOT8P0BEeuf0IcaYj4wxMcaYmMjIyHyEp4pKemYW3y6Pp1eT\nKvbZm/RU2x1Kk2shvIbb4akC6NkokqbVw/ngj6126IKY4ZBx0rZYU6qA8pNw4oHaHq9rAXtym8e5\nb1MeOORM/8MYc9AYcwKYDrS72KCVu37beICDx9O4NcbZHdZOgpOHoMM97gamCswOXVCPrYkpzNqw\nH6q3hpox9pkcbTygCig/CWcp0FBEokUkCLgd+N5rnu+B09dUbgZmG2MMMANoJSJlnUTUE1hfsNCV\nWybG7iayXDCXN460B6FFH9gWTdE93A5NFYLrWlandqUyZ4cuiBkOBzfDjnluh6aKuTwnHOeezIPY\n5LEBmGiMWSciz4vIjc5so4HKIhIHPAo85bz3MPA6NmmtBJYbY6YV3mqoonLgWCq/bUrkpna1CPD3\ns12g7F8Dne7TftNKiAB/P+7pXo8Vu46wZPshaDEQQirYJtJKFUBAfmY2xkzHXg7znPaMx9+pQI4d\naBljvsA2jVbF2LfLE8jMMtwa4zQWWPQ+lKkErW51NzBVqG5pX5u3Zm3hgz+20mlYR2gzCJZ8CMn7\noVxVt8NTxZT2NKDyzBjDN7G76RBVkXqRYXB4J2yabptCB5ZxOzxViMoE+TP0sih+25TIhr3H7DDh\nWRmw/DO3Q1PFmCYclWexOw+z7WDK2cYCSz4CRHsWKKHu7lKXskH+fPjHVohoCPV7wdKPdXA2ddE0\n4ag8+3qp7ajzulbV7RDSyz+3nTyW934cS5UEFcoGcWfHOvywei+7D52ALg/A8f2wdrLboaliShOO\nypPjpzKYtnovN7SuQdmgAFj1FZw6Cp3/5HZo6hIa0T0aP4HR87ZD/d4Q2QQWvatNpNVF0YSj8uTH\nVXs4me501JmVBYs/gBrtdAjpEq56+TL0a1OTCUt3cehEOnS+H/atgR1z3Q5NFUOacFSeTIzdTYMq\nYbStXQG2/gpJcbZ2o02hS7z7etYjNT2LTxfssK0Ry0bAwnfdDksVQ5pw1AXFHUhm+a4j3BbjdNS5\n6H3bK3Sz/m6HpopAgyrluLpZVcbO286hNH87uN7mn+FgnNuhqWJGE466oK+X7rYddbarCYmbbA2n\nwwgICHI7NFVEHr+mMSfSM3lr1mbbKtE/CBa953ZYqpjRhKPOKz0zi8nLE+jdtAoRYcGw4G0ICLHd\nnahSo2HVctzeoTZfLt7F1pNl7aW1lePhxCG3Q1PFiCYcdV6/bjhAUorTUWfyPlg90T51Hhrhdmiq\niP3lqkaEBPrz8vSNtvFAxkk7LIVSeaQJR53XN7G7qVIumJ6NIm3LtKwM+zyGKnUiwoK5/4r6zNqw\nnwXHq0K9K2DxR5CR5nZoqpjQhKNytf9YKr9tOsBN7WsRkJFiR35segNUru92aMolw7tGU7NCGf49\nbQNZnR+A4/vsAG1K5YEmHJWrb5fHk2Wwl9OWjbMPenb9s9thKReFBPrzRJ/GrNtzjMnHmtgHQRe8\now+CqjzRhKNyZDvqjKdjVCWiKzotkup2g5rt3Q5NueyGVjVoXas8r/2ymbROD8GBdbB5htthqWJA\nE47K0dIdh9l+MMX2LLD2WziWoLUbBYCfn/D09c3YdyyVjw63h/K1Yd7rWstRF6QJR+Xo66W7CQsO\n4NoWVWH+2xDZFBpe5XZYykd0iKpEn+bVeG/uTpLb3Qe7F8POBW6HpXycJhx1juTUdKav2csNratT\ndtfv9pLJZQ9pNzYqm6f6NiE9M4tXD3S03d3Me93tkJSP04SjzvHj6r22o872teCPV+0lk5Y5DuSq\nSrGoiFAGd4nii+WJHGg+DOJmwd5VboelfJgmHHWOr5fupmGVMNpkrIb4JdDtEe3GRuXooV4NCA8J\n5J97umCCysG8N90OSfkwTTgqm837k1m5+wi3daiNzPk/KFcd2tzldljKR1UoG8TDvRsyY2squ+rf\nDuunQtJWt8NSPkoTjspmotNR582Ru2HnPNsyLTDE7bCUD7u7c12iKpfl8d3dMH6BMF9rOSpnmnDU\nGWkZWUxZkcCVTatSYckbEBoJ7Ya4HZbycUEBfjzVtwlLDgayueYA26nn4R1uh6V8UL4Sjoj0EZFN\nIhInIk/lUB4sIl875YtFJMqrvI6IHBeRvxYsbHUpzN64n6SUNEbWS4Jtv9mWaUFl3Q5LFQPXNK9G\nx6hKPJJwBUb8Yc5rboekfFCeE46I+APvAn2BZsAdItLMa7YRwGFjTAPgDeA/XuVvAD9dfLjqUpoY\nG0/V8GDa7fgEylSCmBFuh6SKCRHhH9c1ZUNKOZZF9rO1nEPb3A5L+Zj81HA6AnHGmG3GmDRgAtDP\na55+wDjn70lAbxH78IaI9Ae2AesKFrK6FPYdTeX3TQe4v/Fx/LbMgC73Q3CY22GpYqR17Qr0b1OD\nR+KvsPdytJajvOQn4dQEdnu8jnem5TiPMSYDOApUFpFQ4EnguQt9iIiMEpFYEYlNTEzMR3iqIE53\n1HnLsc8gpAJ0HOV2SKoYerxPExKpyB/h18OqCdpiTWWTn4ST02Pm3p0n5TbPc8AbxpjjF/oQY8xH\nxpgYY0xMZGRkPsJTF8t21Lmbu2vuoezOX6HbXyCkvNthqWKoZoUyjOgWzeN7e5HlF2gfHFbKkZ+E\nEw/U9nhdC9iT2zwiEgCUBw4BnYBXRWQH8AjwdxF58CJjVoVs8fZD7EhK4WHzFYRV1dqNKpA/XV4f\nE1aFacHXYdZMhINb3A5J+Yj8JJylQEMRiRaRIOB24Huveb4HTrejvRmYbazuxpgoY0wU8CbwkjHm\nfwWMXRWSLxbt5JrgdUQeWgY9HteWaapAyoUE8siVjXj20JVk+gXD76+4HZLyEXlOOM49mQeBGcAG\nYKIxZp2IPC8iNzqzjcbes4kDHgXOaTqtfMumfclMX5PAc6GToEJdfe5GFYrbO9SmUpWafO13Layd\npH2sKQDE+PAYFjExMSY2NtbtMEq0P32xjJAtP/KGvA4DPoTWt7sdkiohftt0gD+P/Z0l5f5KSO12\nMHiq2yGVGiKyzBgT43Yc3rSngVJsbcJRflmbwNNlJ9uhgrVHaFWILm8USeuGdXk7fYB9kDjuV7dD\nUi7ThFOKvTFzM4NC5lP55A7o9TT4+bsdkipBRIS/X9uU0aeu4HBQDZj5L8jKcjss5SJNOKXUil2H\nWbhxF08GfQO1OkCT690OSZVATauH0799PZ47MRD2r4E1E90OSblIE04p9frMzTxSZjqhaUlwzcs6\nmqe6ZP52bROWlr2cjX71yfr1BUhPdTsk5RJNOKXQku2HiNuyieHyI7S4CWp3cDskVYJVKBvE24Pa\n88KpO/A7Fo9Z8pHbISmXaMIpZYwx/PeXTTxdZhL+YqD3v9wOSZUC7etWovvVA5md2Yb0316F49pt\nVWmkCaeUWbA1iRM7YrnO/IF0uR8q1nU7JFVKjOpej5m1H0LST3Doh6fdDke5QBNOKWKM4b8zNvBy\nyDhMaCR0e9TtkFQp4ucnPD7oRib6X0eFTV+Tsn2x2yGpIqYJpxT5fVMiDfd8RwuzBbn6RQgJdzsk\nVcpUCg2i8W0vctCU58DXf8ZkZbodkipCmnBKCWMMH81Yyt8CJ5BVuzO0us3tkFQpFdO4Lqub/IXo\n1A0smvKu2+GoIqQJp5SYsW4/1yeOJlxO4Hfdf7UZtHJVr1sfYktQUxqufo1N23e6HY4qIppwSoGs\nLMO0n37kjoDZduiBai3cDkmVcn7+/kTc/j8qSDJx4x8j5VSG2yGpIqAJpxSYtmoXf0p+m7SQCPyu\n+Jvb4SgFQMV6MexvNoLr0mcy9ssv8OWOhFXh0IRTwmVkZrH/p1dp5reToBvf0JE8lU+p2f85jgbX\noO+OV/h28Ta3w1GXmCacEm723Hncfepr9tbqg1+zG9wOR6nsgkIJu+kd6vvtZd/0f7N5f7LbEalL\nSBNOCZaekUG1OU+Q5hdMtdvedjscpXLk3+hKUpsM5F6/73jts285kab3c0oqTTgl2KrJr9EqawO7\nOz6NlKvqdjhK5SrkhtcwIRX4S/J/eX7KCrfDUZeIJpwSKm3fBlqu/y/LAtvT9Jp73Q5HqfMLrUzQ\ngP/R1G8Xtda8w+Tl8W5HpC4BTTglUUYax8YPJ8UEkXHD/xA//ZpVMdC4L1mtB3F/wA9MnDqZuAPH\n3Y5IFTI9EpVAGb+9QsSx9Yyp+AgdWzZ1Oxyl8syv7yuYcjX4j997/PXL+aSma9c3JYkmnJJm12L8\n5r/BNxk96H7jcER7FFDFSUg4/gM/oA77uOvQ/3juh3VuR6QKkSackuTEIbImDWMPEfxS9y90qlfZ\n7YiUyr/o7kiPx7nZfw6pseP5bmWC2xGpQpKvhCMifURkk4jEichTOZQHi8jXTvliEYlypl8lIstE\nZI3zf6/CCV+dkZUFU+7FJB/gT6ce5v5r2rodkVIXr+eTZNW5jJeCx/LR5BmsTTjqdkSqEOQ54YiI\nP/Au0BdoBtwhIs28ZhsBHDbGNADeAP7jTD8I3GCMaQkMAT4vaODKy/w3YMsvvGKGUKVxZ9rWqeh2\nREpdPP8A/G4eTVBwWd7wf4uhH/3Bwq1JbkelCig/NZyOQJwxZpsxJg2YAPTzmqcfMM75exLQW0TE\nGLPCGLPHmb4OCBGR4IIErjzsmAezX2RjxNV8nHoFf7mqkdsRKVVw4TXwH/ghDc1OXgn6hCFjFzNj\n3T63o1IFkJ+EUxPY7fE63pmW4zzGmAzgKOB9I+EmYIUx5lT+QlU5OrwTJg4ms2I9hiQOok/z6rSo\nqf2lqRKi0dVIr39wZfofPFX+V/70xTImxu6+8PuUTwrIx7w5NXfy7t71vPOISHPsZbarc/0QkVHA\nKIA6derkI7xS6FQyfHUHZGUwtvZLHNibobUbVfJ0/yvsXc2wjWNIrFWfJybB4ZQ07u1Z3+3IVD7l\np4YTD9T2eF0L2JPbPCISAJQHDjmvawFTgMHGmK25fYgx5iNjTIwxJiYyMjIf4ZUyWVkweRQkbmRt\n17d5ZWkm/VrXoHG1cm5HplThEoH+7yORTXgi+T8Ma5LOyz9t5OWfNuiQBsVMfhLOUqChiESLSBBw\nO/C91zzfYxsFANwMzDbGGBGpAEwD/maMmV/QoBUw61+waTqJ3Z7ljl/LUC8ylOf768BqqoQKDoPb\nxyN+ATxz5J/c2y6UD//YxlPfriEjM8vt6FQe5TnhOPdkHgRmABuAicaYdSLyvIjc6Mw2GqgsInHA\no8DpptMPAg2Af4rISudflUJbi9Jm4buw4G1Oth7KwNjmBAf4M2ZoB8JDAt2OTKlLp1I0DJqIpBzk\nqcP/4rGeNfg6djcPjF+uPRIUE+LLVdKYmBgTGxvrdhi+ZdXXMGUUmU1u4LakUazdl8KEUV1oU7uC\n25EpVTQ2/QwT7oD6vRlb5yWem76FLvUq89Hg9pTTky4ARGSZMSbG7Ti8aU8DxcmWmfDd/Zio7jyW\n8SCxu5N549Y2mmxU6TsGNa0AABDHSURBVNK4D1z3OsTNZNi+f/PmLc1ZuuMQd3y8iIPHtfGrL9OE\nU1zE/QoTBkGVZrwT+RxT1ybxVN8m9G1Z3e3IlCp6McPgqhdg/VT67/g3H9/VlrgDx7nlg4XEHz7h\ndnQqF5pwioO4Wbb5c0Qjvmv1Lq/P3cftHWpzb496bkemlHu6Pgy9noY1E7li84t8MbwDScdPcfP7\nC3Woah+lCcfXbZkJX90JkY1Y2vNT/jotnm4NInihfwvtCVqpHo9Djydg5RfELP8bX4+MIdMYbvlg\nIct3HXY7OuVFE44vWz0RvrodIhuz/bqvGPnNNqIqh/LuoHYE+utXpxQAV/wdev0T1kyk6Zz7mTyy\nLeXLBDLo48X8sTnR7eiUBz1q+aoF78Dke6BOFw7fMpmhE+II8BPGDO1A+TLaEkepM0Sgx1/huv/C\n5hnUnn433w5rRlREKCPHLeXjOdtI12d1fIImHF+TmQE//w1+eRqa9Sf1toncM3EL+46m8vGQGGpX\nKut2hEr5pg4j4aZPYPcSIidcx8SbI+nWIIJ/T99A37fmMkdrO67ThONLThyCL2+GRe9Bp/swN4/h\nye82EbvzMK/f2oZ2OuSAUufX8mYY/B2cSKLc59cwpucJPhkcQ1pGFoPHLOGez2LZlaSt2NyiCcdX\n7F8HH/9/e3ceXWV5J3D8+8tyISHkhoQluSFhUYIQNlEQXCoddlzQ1gqd8dQZPVqLjKWtHu3xjHUc\nT1vqcTx1qmO1rm2PWNFqRFpAUHQoUpYJW1gSIAxZCJBALiQkZHnmj+cF7wn3QnLJfW9u/H3OuSfv\nfd/nzfs7z7v83ve5z/u+34SD6+CW52H2Yp5bvY8PCyt4ZOZwbhqj3Z+VapfB18F9a6B3JvKHbzPt\nxLusXHQDj8wczrqSY0x7bi3PrNhNXWNztCP92tGEE23GwKbX4ZWp0NQA/7wcrrqb97eU8fzqYu68\neiALpuhTcZXqkPQhcO8qyJsFKx+n59K7ePCadNb8ZAo3jc7ihU/3MfXZtXxYWK4PAHWRJpxoqq+B\nd+6CZYsg9xr4/lrImcCG/dU8+t42Jg/N4OnbRmv3Z6XC0TMV5v0BZi2297K9dAOZxzfx3LxxLH1g\nMn17e/jhkkLu/O16fYW1S/RZatGy+2P4+CdQdwym/QwmPQhxcRw4VsftL64jo5eH939wHd5k7ZGm\n1CUr3wJL74HjB2DCfTDtSVoSe/HupkP8asUejtefYf6EXB6ekUdGSuy/jLirPktNE47bTh6G5Y/A\nrgLonw+3vQi+cYB9qdTtL67D39DMBwuuIzdDe6Qp1WnO1MHq/4ANL0Fajn0e27Dp1J5u4tefFPPm\n+lJ6eeL58fQ87po0iIQYvtdNE04YulXCaW6EDb+Fz5+xw1MehWsfgnh7BVN2vJ5FSwrZVl7L2/dd\nw1WD0qMcsFLd1MH1ULAQqksgbzbM+jmkD6W46iT//lER/1NyjLwBKfzslnyuu7xvtKMNiyacMHSL\nhGOMvZpZ9QQcL4VhM2DmL6Dv5QCcqD/DC5+W8ObfDiICz945lpvH+KIbs1LdXfMZe/vB589ASxNM\nvA+u/zEmOZ2VRVU8/XERh2pOM3loBrdd6WNWflZMNW9rwglDTCec1lbY8zGsXQyHt0P/kTDjabh8\nKgANTS28tb6U36wp4WRjM3eMH8iPpufhS0uKbtxKfZ34K2H1U7BtCSQmw6QFMHkBDQmpvL6ulCUb\n/4+D1fUkxgs35vXjlrE+po0YQK8eCdGO/II04YQhJhNOUwPseM+ePVXtgPTL7AMGR38H4hNobTV8\nUFjOsyv3Un7iNN8c3o9HZ1/BFZmp0Y5cqa+vI7vhs59D0YeQ2AuuvAsm/QDTZzDby2spKKxg2bZK\nDvsbSEqMZ+qI/twy1seU4f3okRAf7ejPowknDDGVcE4cgk2vwuY34XQN9BsB1/8IRn0b4u3Z0BfF\nR/nF8t0UVfoZne3lp7Ov4NoYbSNWqls6vN2+wn37UmhthhE3215tg2+gFWFjaQ0FWytYvr2S4/VN\n9O6ZwMz8TG4d6+PayzK6TEcDTThh6PIJp8EPu5fZpzofWGvHDZ8D13wfBt9gHyoI7CivZfFfd/NF\n8TFy0pN4eMZwbhnjIy5O769RqkvyV8LGV2DTa3D6OHhzYMw8GPePkHEZTS2trCs5RsHWClburOJU\nYzMZvTzMGZ3FreN8XJXbJ6r7tyacMHTJhFNfY9++uXsZ7P0rNDdAn8G2yWz89yAt91zRsuP1PLty\nLx8UluNNSuRf/2EYd03K7ZKX4EqpIJpO23vmtr4N+9aAaYWscXDFTfbkckA+Dc2tfLbnCB9treST\nXVU0Nrfi8/Zk+sgBjMr2Mirby+X9U1x9pYgmnDB0iYTTfAYqt9ormOKVULbRbnS9+kH+7TbRDJxw\n7moGoLa+iRc+K+GNdaWIwD3XD+GBGy/T1wooFcv8lbD9T7DrI3scAHuCOWyGbdEYfD2nEtL4pKiK\ngq0VrN9XzemmFgA8CXEMH9CbfF+q/WR7GZGZSpInMiefmnDC4HrCMQZOVtp23PLNcPBvULYJmk/b\n6VnjIG8mDJsJvish7qszlpZWw4FjdazeVcWLn+3D39CkPc+U6q5OVtkWjj3L4cAX0FRnx/cfCbmT\nIGscLZljORCXy86q0+ys8LOzopadFX5O1DcBECcwtF8K+b5URvm8TjLydkr3a004YYhYwjEG6o5C\n9T6o2QdH98DhbTbR1FfbMhIHmaMh91oYNBlyJ0NKfwDqGpvZffgkRZV+iir8FFX62XPYT0OTfcmT\n9jxT6mukpQkqCqH0C/sp2wyNzrPZ4j0wIB8yx0DfYZiMy6lKzGFbXRo7DtdT5CShytqGc/8uOy2J\nUdmp/NvNIxnYJ7ynjXSLhCMis4BfA/HA74wxv2wzvQfwFnAVUA3MM8aUOtN+CtwLtAAPGWNWXGx5\nYSecxlP2SsVfcf7f2kNQvR/OnPyqfLzHnplkjrYbRtYYGJCP8aRw5GTjuaRSVOlnV4WfA9V1nK02\nb1IiI7J6MzLLy0hfKmMGeskb0LvjMSuluofWVvvMtspCm4gq/heOFH11MgsQlwh9BkFqNqRmU5+U\nSXlLH/Y2eNnmT2LTUQ+vPTgbb6/wnusW8wlHROKBvcB0oAzYCHzXGFMUUGYBMMYY84CIzAduN8bM\nE5GRwNvARMAHfALkGWNaLrTMsBPO63Pse2UCmB6ptKZk0ZTiozF1MHUpgziZPIgTSTmc8GRS1yzU\nn2nh9JkWjp5qZJdz9VJdd+bc/8hJT2JkVuq55DLSl4rP21Of5qyUurj6Gvs4neoSOFYMNfvtSbC/\n3J4QmzavwV64+dwTSTqqqyacjtwuOxEoMcbsBxCRJcBcoCigzFzgSWd4KfAbsUfjucASY0wjcEBE\nSpz/t/7Swg/uDXMTZT0mUN6cxqHmNEqbvJxq6AFBn0B+xPl8xRMfR15mClNH9LcJxufliqzepPbU\nH/2VUmFKTofkiZAz8fxpLc1wquqrBFR3FFK73yOuOpJwsoFDAd/LgGtClTHGNItILZDhjP+yzbzZ\nwRYiIvcD9wPk5uYGK3JR/kEzOJp8ijRPPFmJCdzoiSPZk0BSYjzJnniSPPHOcAJJHmdcwLRkTwLx\neo+MUsot8QngzbYfJkQ7mojpSMIJdgRu2x4Xqkx75rUjjXkZeBlsk1oH4jvnoanDwplNKaVUBHXk\nTqQyICfg+0CgIlQZEUkAvEBNO+dVSinVjXUk4WwEhonIEBHxAPOBgjZlCoC7neE7gDXG9kooAOaL\nSA8RGQIMA/5+aaErpZSKJe1uUnN+k1kIrMB2i37NGLNTRJ4CNhljCoBXgd87nQJqsEkJp9yfsB0M\nmoEHL9ZDTSmlVPfy9bzxUymlurGu2i26azxLWymlVLenCUcppZQrNOEopZRyhSYcpZRSrujSnQZE\n5ChwMMzZ+wLHOjGczqJxdYzG1TEaV8d017gGGWP6dVYwnaVLJ5xLISKbumIvDY2rYzSujtG4Okbj\ncpc2qSmllHKFJhyllFKu6M4J5+VoBxCCxtUxGlfHaFwdo3G5qNv+hqOUUqpr6c5XOEoppboQTThK\nKaVcEfMJR0RmicgeESkRkceCTO8hIu840zeIyGAXYsoRkU9FZJeI7BSRHwYpM0VEakWk0Pk8Eem4\nnOWWish2Z5nnPRlVrOed+tomIuNdiGl4QD0UiohfRBa1KeNKfYnIayJyRER2BIxLF5FVIlLs/O0T\nYt67nTLFInJ3sDKdHNczIrLbWU9/FpG0EPNecJ1HIK4nRaQ8YF3NCTHvBffdCMT1TkBMpSJSGGLe\nSNZX0GNDV9jGXGGMidkP9jUJ+4ChgAfYCoxsU2YB8JIzPB94x4W4soDxznBvYG+QuKYAy6JQZ6VA\n3wtMnwP8BfuW1knAhiis08PYG9dcry/gG8B4YEfAuF8BjznDjwGLg8yXDux3/vZxhvtEOK4ZQIIz\nvDhYXO1Z5xGI60ng4Xas5wvuu50dV5vpzwJPRKG+gh4busI25sYn1q9wJgIlxpj9xpgzwBJgbpsy\nc4E3neGlwFQRCfbK605jjKk0xmxxhk8Cu4DsSC6zE80F3jLWl0CaiGS5uPypwD5jTLhPmLgkxpjP\nse9yChS4Db0J3BZk1pnAKmNMjTHmOLAKmBXJuIwxK40xzc7XL7Fv0nVViPpqj/bsuxGJy9n/7wTe\n7qzltdcFjg1R38bcEOsJJxs4FPC9jPMP7OfKODtnLZDhSnSA04R3JbAhyOTJIrJVRP4iIvkuhWSA\nlSKyWUTuDzK9PXUaSfMJfSCIRn0BDDDGVII9YAD9g5SJdr3dg70yDeZi6zwSFjpNfa+FaB6KZn3d\nAFQZY4pDTHelvtocG2JhG7tksZ5wgl2ptO3n3Z4yESEiKcB7wCJjjL/N5C3YZqOxwH8BH7gRE3Cd\nMWY8MBt4UES+0WZ6NOvLA9wKvBtkcrTqq72iWW+PY9+k+8cQRS62zjvbfwOXAeOASmzzVVtRqy/g\nu1z46ibi9XWRY0PI2YKMi6n7WmI94ZQBOQHfBwIVocqISALgJbwmgA4RkUTsBvVHY8z7bacbY/zG\nmFPO8HIgUUT6RjouY0yF8/cI8Gds00ag9tRppMwGthhjqtpOiFZ9OarONis6f48EKROVenN+OL4Z\n+CfjNPS31Y513qmMMVXGmBZjTCvwSojlRau+EoBvAe+EKhPp+gpxbOiy21hnivWEsxEYJiJDnLPj\n+UBBmzIFwNneHHcAa0LtmJ3FaSN+FdhljPnPEGUyz/6WJCITseuiOsJx9RKR3meHsT8672hTrAD4\nnliTgNqzl/ouCHnmGY36ChC4Dd0NfBikzApghoj0cZqQZjjjIkZEZgGPArcaY+pDlGnPOu/suAJ/\n87s9xPLas+9GwjRgtzGmLNjESNfXBY4NXXIb63TR7rVwqR9sr6q92B4vjzvjnsLuhAA9sU00JcDf\ngaEuxHQ99lJ3G1DofOYADwAPOGUWAjuxvXO+BK51Ia6hzvK2Oss+W1+BcQnwglOf24GrXVqPydgE\n4g0Y53p9YRNeJdCEPaO8F/ub32qg2Pmb7pS9GvhdwLz3ONtZCfAvLsRVgm3TP7uNne2N6QOWX2id\nRziu3zvbzjbsgTSrbVzO9/P23UjG5Yx/4+w2FVDWzfoKdWyI+jbmxkcfbaOUUsoVsd6kppRSKkZo\nwlFKKeUKTThKKaVcoQlHKaWUKzThKKWUcoUmHKWUUq7QhKOUUsoV/w+F9SAHQQO0KwAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279be01c470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_ = 10\n",
    "\n",
    "plt.title(\"Comparison of Poisson and Gaussian distribution for lambda = \" + str(lambda_));\n",
    "xg = np.linspace(0, 2*lambda_, 300)\n",
    "xp = range(2*lambda_ + 1)\n",
    "plt.plot(xp, poisson.pmf(xp, lambda_), label=\"Poisson\")\n",
    "plt.plot(xg, gauss(lambda_, np.sqrt(lambda_))(xg), label=\"Normal\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PyElcgGHZVtM3sSWUpD8c2OJ3v9Rb1p4rgJf97qeJSImILBGRs7oRozFhtbWq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\n2vQJE6recCdIs4ZGO6TQHXU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2QH0VNFT53d4DTR2MZJiStX/nzMx3wxZkDoaBh7gk76vJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x279be0127b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = 1;\n",
    "gamma = 1.75;\n",
    "xg = np.linspace(-4*sigma, 4*sigma)\n",
    "xc = np.linspace(-6*gamma, 6*gamma)\n",
    "plt.title(\"Comparison of Gaussian and Cauchy distribution\");\n",
    "plt.plot(xg, gauss(0, sigma)(xg),label=\"Normal\")\n",
    "plt.plot(xc, cauchy(0, gamma)(xc),label=\"Cauchy\" )\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Центральная предельная теорема"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Центральная предельная теоремма утверждает, что если некоторая случайная величина $x$ имеет распределение со средним $\\mu$ с конечной дисперсией $D$, то сумма большого количества таких случайных величин\n",
    "$\\sum_{i=1}^{n}{x_i}$ будет иметь нормальное распределение со средним $n \\mu$ и дисперсией $n D$ не зависимо от формы исходного распределения.\n",
    "\n",
    "Центральная предельная теорема в общем случае не говорит о том, каким должно быть $n$, обычно это надо определять экспериментально для каждого типа распределения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7j6BFizCPHdvjLt5JSQRceil177yDtloxGUykBCdxyMur625XGD03MYmRQ5K7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\nZgNx/rVYCosIWryYLaVbCPUOJTUs1bH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      "text/plain": [
       "<matplotlib.figure.Figure at 0x279bce0ef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = uniform(-0.5,0.5);# Распределение, над которым мы экспериментируем\n",
    "wind = 1; # ширина окна интегрирования\n",
    "\n",
    "fs = [f];\n",
    "# fs << f;\n",
    "x = np.linspace(-wind, wind, 300)\n",
    "plt.title(\"Central limit theorem\");\n",
    "plt.plot(x, f(x),label=\"Initial distribution\")\n",
    "\n",
    "for i in range(1,6):\n",
    "    wi = (i+1)*wind\n",
    "    fs.append(interpolate(convolute(fs[i-1],f,-wind,wind),-wi,wi))\n",
    "    x = np.linspace(-wi, wi, 300, endpoint=True)\n",
    "    plt.plot(x, fs[i](x), label = \"Convolution \"+str(i))\n",
    "\n",
    "\n",
    "plt.legend();"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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