803 lines
277 KiB
Plaintext
803 lines
277 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "4cd099",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"# Generowanie losowych obiektów w Pythonie. Znane rozkłady prawdopodobieństwa w Pythonie. "
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]
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},
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{
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"cell_type": "markdown",
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"id": "bdfc62",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"## Biblioteka NumPy\n",
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"\n",
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"**NumPy** (Numerical Python) jest biblioteką dla języka Python, której głównym zadaniem jest umożliwienie pracy na dużych, wielowymiarowych tabelach i macierzach. Zacznijmy od zaimportowania biblioteki za pomocą poniższego polecenia."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"id": "1498f3",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"import numpy as np"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ac566b",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"Ponieważ głównym obiektem biblioteki NumPy są macierze, czyli obiekty klasy `ndarray` (N dimensional array), zobaczmy na początek w jaki sposób z nimi pracować. Obiekty tego typu mają zazwyczaj ustalony rozmiar, który wyznaczony jest przez kształt macierzy, czyli `shape`. Np. `shape = (2,2,4)` dotyczy macierzy trójwymiarowej o wymiarach $2\\times 2\\times 4$ i $2\\cdot 2\\cdot 4 = 16$ polach."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"id": "60fe48",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Macierz A\n",
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" [[1 2 3]\n",
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" [2 3 4]] \n",
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"\n",
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"Macierz jedynek\n",
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" [[1. 1. 1. 1.]\n",
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" [1. 1. 1. 1.]\n",
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" [1. 1. 1. 1.]] \n",
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"\n",
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"Macierz zer\n",
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" [[0. 0.]\n",
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" [0. 0.]]\n"
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]
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}
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],
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"source": [
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"# tworzymy macierz typu ndarray\n",
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"A = np.array([[1, 2, 3], [2, 3, 4]])\n",
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"print(\"Macierz A\\n\", A, \"\\n\")\n",
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"\n",
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"# tworzymy macierz o wymiarach 3x4 składającą się z samych jedynek\n",
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"A_ones = np.ones((3, 4))\n",
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"print(\"Macierz jedynek\\n\", A_ones, \"\\n\")\n",
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"\n",
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"# tworzymy macierz o w ymiarach 2x2 składającą się z samcyh zer\n",
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"A_zeros = np.zeros((2, 2))\n",
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"print(\"Macierz zer\\n\", A_zeros)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7ea41f",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"Na macierzach możemy wykonywać standardowe działania takie jak mnożenie, co przyda nam się na późniejszych zajęciach przy okazji pracy z łańcuchami Markowa."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 54,
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"id": "2b527e",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Macierz B\n",
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" [[1 2]\n",
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" [1 4]\n",
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" [5 0]\n",
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" [5 1]] \n",
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"\n",
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"Wektor v\n",
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" [1 2] \n",
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"\n",
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"Wynik mnożenia B przez v\n",
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" [5 9 5 7]\n"
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]
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}
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],
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"source": [
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"# Tworzymy macierz B o wymiarach 4x2 oraz wektor v\n",
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"B = np.array([[1, 2], [1, 4], [5, 0], [5, 1]])\n",
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"v = np.array([1, 2])\n",
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"print(\"Macierz B\\n\", B, \"\\n\")\n",
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"print(\"Wektor v\\n\", v, \"\\n\")\n",
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"\n",
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"# Mnożenie macierzy B przez wektor v\n",
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"result = B.dot(v)\n",
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"print(\"Wynik mnożenia B przez v\\n\", result)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "deb832",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"## Generowanie losowych obiektów w NumPy\n",
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"\n",
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"Na tym kursie interesować nas będzie przede wszystkim zastosowanie biblioteki NumPy w odniesieniu do rachunku prawdopdodobieństwa.\n",
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"\n",
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"Podstawowym narzędziem, z którego będziemy korzystać jest generator liczb (i innych obiektów) losowych (a dokładniej rzecz ujmując pseudolosowych). Aby wygenerować losową liczbę całkowitą możemy posłużyć się funkcją `randint(n)` (zwracającą losową liczbę całkowitą z przedziału `[0, n)` zgodnie z **rozkładem jednostajnym**, czyli takim, gdzie każda liczba z podanego przedziału ma szanse pojawić się z równym prawdopodobieństwem)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "f45d82",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"96\n",
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"75\n",
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"0\n",
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"32\n",
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"51\n",
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"61\n",
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"25\n",
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"4\n",
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"7\n"
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]
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}
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],
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"source": [
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"# generujemy 10 liczb losowych z przedziału [0,100]\n",
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"for _ in range(10):\n",
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" x = np.random.randint(100)\n",
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" print(x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "915a84",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[60 12 38 99 87 40 22 92 79 66]\n",
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" [27 30 90 72 35 52 67 80 51 26]]\n"
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]
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}
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],
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"source": [
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"# generujemy tablicę typu ndarray o wymiarach 2 x 10 wypełnioną losowymi liczbami całkowitymi z przedziału [0, 100]\n",
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"\n",
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"x = np.random.randint(100, size=(2, 10))\n",
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"print(x)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "050663",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"NumPy daje nam również możliwość losowania dowolnych obiektów. Służy do tego funkcja `choice`, która przyjmuje następujące argumenty:\n",
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" - `a` - może być jednowymiarową macierzą typu `ndarray`, wówczas losowane są elementy z tej macierzy, `a` może być też liczbą naturalną, wówczas losowane są liczby naturalne z przedziału `[0, a]`,\n",
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" - `size` - determinuje ile obiektów jest losowanych, może być to liczba lub wektor liczb, domyślnie `size` przyjmuje wartość `None`co oznacza, że losowany jest jeden obiekt,\n",
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" - `replace` - czy losujemy ze zwracaniem, czy bez zwracania, domyślnie przyjmuje wartość `True` co oznacza, że dany obiekt może zostać wylosowany wielokrotnie,\n",
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" - `p` - wektor prawdopodobieństw, jeśli chcemy by losowanie odbywało się nie w sposób jednostajny, tylko ze z góry zadanym rozkładem.\n",
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" \n",
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" **Przykład 1**\n",
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" \n",
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" Chcemy wylosować:\n",
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" - jedną kartę\n",
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" - $5$ kart otrzymanych przez pojedynczego gracza\n",
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" - rozdanie po $5$ kart dla czterech graczy\n",
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" \n",
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" ze standardowej talii $52$ kart. W tym celu najpierw definiujemy talię, a następnie stosujemy funkcję `choice` z odpowiednimi parametrami."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"id": "63563b",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Losowa karta: 10 karo \n",
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"\n",
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"Rozdanie 5 losowych kart dla jednego gracza: ['7 trefl' '7 kier' '5 karo' 'As pik' '2 pik'] \n",
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"\n",
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"Rozdanie po 5 losowych kart dla czterech graczy: \n",
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" [['2 pik' '10 karo' '5 trefl' '9 pik' '8 kier']\n",
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" ['3 karo' '9 kier' '5 kier' '5 pik' '4 karo']\n",
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" ['6 trefl' '2 kier' 'Walet trefl' '4 kier' '6 kier']\n",
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" ['4 trefl' 'Dama kier' 'Król trefl' 'Dama trefl' '7 trefl']]\n"
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]
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}
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],
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"source": [
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"# tworzymy standardową talię 52 kart\n",
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"values = ['2', '3', '4', '5', '6', '7', '8', '9', '10', 'Walet', 'Dama', 'Król', 'As']\n",
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"suits = ['kier', 'karo', 'pik', 'trefl']\n",
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"deck = [v + ' ' + s for v in values for s in suits]\n",
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"\n",
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"# losujemy jedną kartę z naszej talii\n",
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"x = np.random.choice(deck)\n",
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"print(\"Losowa karta:\", x, \"\\n\")\n",
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"\n",
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"# losujemy jednocześnie 5 kart z naszej talii, domyślnie parametr replace = True, co oznacza że losujemy kolejno ze zwracaniem\n",
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"y = np.random.choice(deck, size=5, replace=False)\n",
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"print(\"Rozdanie 5 losowych kart dla jednego gracza: \", y, \"\\n\")\n",
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"\n",
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"# losujemy jedocześnie 5 kart z naszej talii dla 4 różnych graczy\n",
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"z = np.random.choice(deck, size=(4, 5), replace=False)\n",
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"print(\"Rozdanie po 5 losowych kart dla czterech graczy: \\n\", z)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0ca5a9",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"**Przykład 2**\n",
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"\n",
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"Chcemy wylosować $10$ razy ze zwracaniem jedną kulę z urny zawierającej $3$ białe, $4$ czerwone i $5$ zielonych kul. Możemy tutaj zastosować dwa podejścia:\n",
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" - losujemy w sposób jednostajny jeden obiekt z tablicy zawierającej $3+4+5=12$ elementów, które odpowiadają naszym kulom,\n",
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" - losujemy jeden z kolorów zgodnie z rozkładem, który odpowiada częstotliwościom występowania każdego z kolorów, czyli przyjmując wektor prawdopodobieństw $p = (3/12, 4/12, 5/12)$."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"id": "ee00fe",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"['b' 'c' 'c' 'b' 'b' 'z' 'z' 'b' 'z' 'z']\n",
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"['b' 'b' 'b' 'b' 'z' 'b' 'z' 'c' 'z' 'b']\n"
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]
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}
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],
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"source": [
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"# pierwszy sposób\n",
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"kule = ['b', 'b', 'b', 'c', 'c', 'c', 'c', 'z', 'z', 'z', 'z', 'z']\n",
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"x = np.random.choice(kule, size=10)\n",
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"print(x)\n",
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"\n",
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"# drugi sposób\n",
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"kolory = ['b', 'c', 'z']\n",
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"prawdop = [1/4, 1/3, 5/12]\n",
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"y = np.random.choice(kolory, size=10, p=prawdop)\n",
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"print(y)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "01e68a",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"Przeprowadźmy teraz $1000$-krotne losowanie ze zwracaniem kuli z naszej urny i porównajmy częstotliwość wyboru każdego z kolorów z częstotliwością występowania tego koloru w urnie. Proszę zauważyć, że\n",
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"$$(3/12, 4/12, 5/12) = (0{.}25, 0{.}333\\ldots, 0{.}41666\\ldots) = (0{.}25, 0{.}(3)), 0{.}41(6)).$$\n",
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"Jeśli nasz generator faktycznie zwraca obiekty w sposób losowy, spodziewamy się, że uzyskane częstotliwości występowania kolorów podczas losowania będą odpowiadały częstotliwościom występowania każdego z kolorów w urnie."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"id": "664ba3",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Częstotliwość wystąpień koloru białego: 0.252\n",
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"Częstotliwość wystąpień koloru czerwonego: 0.304\n",
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"Częstotliwość wystąpień koloru zielonego: 0.444\n"
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]
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}
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],
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"source": [
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"x = np.random.choice(kolory, size=1000, p=prawdop)\n",
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"\n",
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"# Zliczanie wystąpień konkretnego elementu, np. 'b'\n",
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"b_count = np.count_nonzero(x == 'b')\n",
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"print(\"Częstotliwość wystąpień koloru białego:\", b_count/1000)\n",
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"c_count = np.count_nonzero(x == 'c')\n",
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"print(\"Częstotliwość wystąpień koloru czerwonego:\", c_count/1000)\n",
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"z_count = np.count_nonzero(x == 'z')\n",
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"print(\"Częstotliwość wystąpień koloru zielonego:\", z_count/1000)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "746df6",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"## SciPy\n",
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"\n",
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"**SciPy** jest bogatą biblioteką, która umożliwia wykonywanie skomplikowanych obliczeń tj. całkowanie czy optymalizacja. My natomiast wykorzystamy funkcje związane ze znanymi rozkładami prawdopodobieństwa dostępne dzięki pakietowi `stats`. Będą nas interesowały już poznane rozkłady dyskretne:\n",
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" - rozkład Bernoulliego (dla pojedynczej próby): `bernoulli`\n",
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" - rozkład dwumianowy: `binom`\n",
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" - rozkład geometryczny: `geom`\n",
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" - rozkład Poissona: `poisson`\n",
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" - rozkład hipergeometryczny: `hypergeom`\n",
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" - rozkład Pascala (ujemny dwumianowy): `nbinom`\n",
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" - rozkład jednostajny (na skończonym zbiorze liczb): `randint`\n",
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" \n",
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" a także rozkłady ciągłe:\n",
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" - rozkład jednostajny: `uniform`\n",
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" - rozkład wykładniczy: `expon`\n",
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" - rozkład standardowy normalny: `norm`.\n",
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" \n",
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" Zacznijmy od zaimportowania odpowiedniego pakietu: `stats`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "8a7728",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"from scipy import stats"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a519aa",
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"metadata": {
|
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"collapsed": false
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},
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"source": [
|
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"Omówimy teraz pokrótce niektóre z wyżej wymienionych rozkładów. Przy czym należy pamiętać, że dla każdego z rozkładów zdefiniowane są podobne metody, zatem nie będziemy ich za każdym razem powtarzać. Metody, z których będziemy najcześciej korzystać przy okazji **rozkładów dyskretnych** to:\n",
|
|
" - `pmf` czyli **funkcja masy prawdopodobieństwa** (*ang. probability mass function*),\n",
|
|
" - `cdf` czyli **dystrybuanta** (*ang. cumulative distribution function*),\n",
|
|
" - `mean` czyli **wartość oczekiwana** (*ang. mean value* or *expectation*),\n",
|
|
" - `var` czyli **wariancja** (*ang. variance*),\n",
|
|
" - `std` czyli **odchylenie standardowe** (*ang. standard deviation*) będące po prostu pierwiastkiem z wariancji,\n",
|
|
" - `rvs` czyli funkcja zwracająca **losową próbkę** (*ang. random sample*) zgodnie z rozkładem zadanej zmiennej losowej \n",
|
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" \n",
|
|
" Z kolei do pracy z **rozkładami ciągłymi**, poza wyżej wymienionymi metodami (oprócz `pmf`, która nie ma sensu dla rozkładów ciągłych) przyda nam się dodatkowo metoda:\n",
|
|
" - `pdf` czyli **gęstość rozkładu** (*ang. probability density function*).\n",
|
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"\n",
|
|
"### Rozkład dwumianowy stats.binom\n",
|
|
"\n",
|
|
"Przypomnijmy, że rozkład dwumianowy $Bin(n,p)$ z parametrami $n$ i $p$ dotyczy $n$ niezależnych prób Bernoulliego z prawdopodobieństwem sukcesu w pojedynczej próbie wynoszącym $p \\in (0,1)$, a zmienna losowa o tym rozkładzie zwraca liczbę uzyskanych sukcesów. Do wygenerowania takiej zmiennej losowej służy funkcja `stats.binom` przyjmująca dwa argumenty $n$ i $p$.\n",
|
|
" \n",
|
|
" **Przykład 3**\n",
|
|
" \n",
|
|
" Wyznaczymy funkcję masy prawdopodobieństwa, wartość oczekiwaną oraz wariancję zmiennej losowej $X$, która zlicza liczbę czwórek wyrzuconych w $12$ rzutach standardową kostką. Wiemy zatem, że $$X \\sim Bin(12, 1/6).$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "8ebffc",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Funkcja masy prawdopodobieństwa zmiennej losowej X\n",
|
|
"P(X = 0 ) = 0.11215665478461513\n",
|
|
"P(X = 1 ) = 0.2691759714830762\n",
|
|
"P(X = 2 ) = 0.29609356863138386\n",
|
|
"P(X = 3 ) = 0.19739571242092233\n",
|
|
"P(X = 4 ) = 0.08882807058941508\n",
|
|
"P(X = 5 ) = 0.028424982588612827\n",
|
|
"P(X = 6 ) = 0.006632495937342999\n",
|
|
"P(X = 7 ) = 0.001136999303544513\n",
|
|
"P(X = 8 ) = 0.00014212491294306426\n",
|
|
"P(X = 9 ) = 1.263332559493902e-05\n",
|
|
"P(X = 10 ) = 7.579995356963424e-07\n",
|
|
"P(X = 11 ) = 2.7563619479866997e-08\n",
|
|
"P(X = 12 ) = 4.593936579977831e-10\n",
|
|
"Wartość oczekiwana zmiennej losowej X = 2.0\n",
|
|
"Wariancja zmiennej losowej X = 1.6666666666666667\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# definiujemy zmienną losową X o dwumianowym rozkładzie prawdopodobieństwa z parametrami n=12 i p=1/6\n",
|
|
"X = stats.binom(12, 1/6)\n",
|
|
"print(\"Funkcja masy prawdopodobieństwa zmiennej losowej X\")\n",
|
|
"for k in range(13):\n",
|
|
" print(\"P(X =\", k,\") = \", X.pmf(k))\n",
|
|
"print(\"Wartość oczekiwana zmiennej losowej X = \", X.mean())\n",
|
|
"print(\"Wariancja zmiennej losowej X = \", X.var())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "66310d",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"### Rozkład geometryczny\n",
|
|
"\n",
|
|
"Rozkład geometryczny $Ge(p)$ z parametrem $p\\in(0,1)$ dotyczy eksperymentu, w którym powtarzamy niezależne próby Bernoulliego z prawdopodobieństwem sukcesu w pojedynczej próbie równym $p$, do momentu uzyskania pierwszego sukcesu. Zmienna losowa o tym rozkładzie zwraca liczbę takich prób i możemy ją wygenerować za pomocą polecenia `stats.geom`. \n",
|
|
"\n",
|
|
"**Przykład 4**\n",
|
|
"\n",
|
|
"Przedstawimy na wykresie funkcję masy prawdopodobieństwa zmiennej losowej o rozkładzie geometrycznym z parametrem $p=1/8=0{.}125$. Do rysowania wykresów korzystać będziemy z biblioteki **matplotlib**."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"id": "51c8a4",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
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",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 18,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 440,
|
|
"width": 726
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# definiujemy zmienną losową Y o rozkładzie geometrycznym z parametrem p=0.125\n",
|
|
"Y = stats.geom(0.125)\n",
|
|
"\n",
|
|
"# wartości do wykresu\n",
|
|
"x = np.arange(1, 26)\n",
|
|
"pmf_values = Y.pmf(x)\n",
|
|
"\n",
|
|
"# tworzenie wykresu\n",
|
|
"plt.bar(x, pmf_values)\n",
|
|
"plt.title('Funkcja masy prawdopodobieństwa zmiennej losowej Y')\n",
|
|
"plt.xlabel('k')\n",
|
|
"plt.ylabel('P(Y=k)')\n",
|
|
"plt.xticks(x)\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fd54b0",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"### Rozkład Poissona\n",
|
|
"\n",
|
|
"Zmienna losowa $X$ ma rozkład Poissona z parametrem $\\lambda\\in (0,+\\infty)$, jeśli jej funkcja masy prawdopodobieństwa dana jest wzorem:\n",
|
|
"\n",
|
|
"$$\\mathbb{P}(X=k)=\\frac{\\lambda^k}{k!}e^{-\\lambda} \\quad \\text{ dla } \\quad k=0,1,2,\\ldots$$\n",
|
|
"\n",
|
|
"Rozkładu tego używamy najczęściej aby modelować zdarzenia ,,rzadkie'' np. liczbę wypadków drogowych, liczbę pożarów budynku itp. Wówczas parametr $\\lambda$ odnosi się do średniej wartości tej zmiennej losowej. Zmienną losową o tym rozkładzie wygenerujemy za pomocą polecenia `stats.poisson`.\n",
|
|
"\n",
|
|
"**Przykład 5**\n",
|
|
"\n",
|
|
"Porównajmy ze sobą rozkład Poissona i rozkład dwumianowy. W tym celu rozważymy zmienną losową $X \\sim Bin(n, \\frac{\\lambda}{n})$ oraz zmienną losową $Y \\sim Po(\\lambda)$, tak żeby\n",
|
|
"$$\\mathbb{E}(X) = n\\cdot\\frac{\\lambda}{n} = \\mathbb{E}Y.$$\n",
|
|
"\n",
|
|
"Wygenerujemy funkcje masy prawdopodobieństwa dla obu tych rozkładów i dla porównania przedstawimy je na jednym wykresie. Jak się okazuje, dostajemy bardzo podobny rozkład prawdopodobieństwa, co nie jest przypadkiem, ponieważ rozkład dwumianowy $Bin(n,p)$ można dobrze przybliżać rozkładem Poissona $Po(\\lambda)$ przy założeniu, że $p = \\frac{\\lambda}n$. Jako ćwiczenie proszę pozmieniać parametry $\\lambda$, $n$ i $p=\\frac{\\lambda}{n}$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 43,
|
|
"id": "581700",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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9YhGxLVnge1HgrJTSoRXq+37+eFdK6c72drbIPvnj+SmlLyrkuTp/rDjvbCt+lVL6snhFSmkO2U+gIQsE/bFMufvyx+WjZE7vluT77bb83xElyf/JH5eutj6yKQ0AvhkRSxYnRMSqZKPTE3BFG+os9jpZUKiJlNK/gd/m/1aav3M2cE4724XsSxUo2U8ppc/IfoIKjXMEF/89keyLjgC2KJP+YEk7hf4/kVJ6oLQTKaWXyX6pUM7WZKPK/gv8okzZ2WSj9QE2j4hBFeo5O6X0eZn155AFGxYh+wBdi3bnxe1tSeE6cWlK6ZMKeQrXiS3LzflKNtVPueP8bbJRmtD0OvkpWYAH2na+VuOh/LHh2I6IxchG6k4hG+FZmr4i2Uj3L2jDDcZauR7NTWfn191Sw8mCs5AFPcs5JX8cShYAqiiy+dYvz//9SUrp1hby9iEbwb8n8E9g85TSc2XyfZssYAtwXUppn5TSpy31oyA/B+7J/y3d/x05T1tTqPv6lNKLZep+mMbjsNQTZOf/oGh6X4PC8XgD2ZdSa0TT+1dUuv7WyhmlK1JKb5B96QHwl3yflSq8lrf4PqiNCq9dG1e43gA8nFJ6pHRlSmkS2fuOJn3K5xjeNf/33JTSzDJ1Xga8Rfba1/C6XOvXzJTSM8Bksvey3yvTj33zxwkV3ivOFfmc4StHxBk0nqOP5/sYGvfRZSmld0vLp5TupvF6+u0qm23r+7hC/gXIfj1SjV3IBle8S+N7wAb5sVF4ff5WC8dgs3Mmd1P+2KZzIqX0GtmXcH3Jrt2SVBWD1pJUfx5MKUWFZedOaK/ZTb1yb+WPLQXKdyeb87Av2fzCx7WQd+P88fa2da+5/AY/hQDEb/Ob/jRbgOvzPMu2s6n/q7D+vfzx+QrBlH8V/T2gNDEiBkd2g6dJ+U1qZhfdYOjcPFvpDbgK++2IiLgqspsU9m+p8yml/yMLqpX78Lhf/nhfSun1luppwYMtfOgsfJBdM8rf0PPlPLhdUUT0iezmnBMju4nVF0X76Zk8W7kblRXaLvcB/MEq0outW2F9ufZKFco+l1L6qEKeh8gC+MX5S00stzKl9B8a90Nx2Y60Oy9ub0s2zR9PbOE6UbgG9qV8YODpFo7zZtfJPChQ2Ed3RcSJETG8heBAWxTqXT/yGzmSjXztkac9RzYSffOim3MVju2nygWz2nk9mpsqBdoLx8D7KaV/lMuQB13fKsnfTP6l3o1kc9v+KaV0Zgv9WYRs6o5vkgU9N0spTS1T50/JAscL56vKBqsjYlhEXBQR/xvZDT7nFO3/cXm20v3fkfO0Ne2uO6U0i5IAaB5Q3ZxsmoPJedmGAGj+BUDh9bwzgtaf0RicLlV4Lf97hfTCa3mbBgxERK/8Jnh3Rnbz0M+LntPCtbF3C/VWel8G5d+brUA2cACy6R+ayd+rTMz/LT0XavmaCY3B0n2LV0Z2c+yNyb7Um1Cun51sn6Ln4UuyX9MdR/YroBfJvoQif89SCMqW3Z+5wgCGal+P2vo+7qV8WRB4PH8/NKzSjRBL+vJw/kVxS/3uRzY1SqkPU0qvVijb4meDiNg6sptxvxKNN2Yt7PO182xd+XoiaR5j0FqS5nMppekVkj7LHxdoofgvyN5MX97Kh3zIRopDNmqxowbm7UIWZKo0Mn2JPE9771j+ToX1s1tKL/mg0GT/RcRIshGRPyb7cLEo2Yf5f+VLYWRNkxHaKaU/kM2DG2QB6NuBjyPimYg4NSIqjdxp9uExD57tnf97ebMS1XurirSelP9w835LFefb8yzZ6NqRZDfK+jwv9y+y6UegZD/lmnzAzj/gbUEWNJpEFjhNRem9aQyalI4g/Er++HYL3a20H77SSnphlFthW75SIVs1+7m4bEfanRe3tyWF82IAla8TSxXl70tzla6RUPk6eQDZeb4k2ejyZ8jO19si4nv5F29tlo8GfTtvrxCQbxgRmQemHibb3rVK0puNjm3v9aglEbFHC18QtEela0Wrx1uuMDK17DETEQuQzWm8LNn1Yb9y+YrsQnY9+YJsqqtKr2kPkE3ZcHaliiJiT7Kf2x9GNlq+H9mXDoX9PyPPWrr/O3KetqajdZcGONcke51+NP/lUmn6xmSv5++klCoFlzviXy186dTia3lRekvvg5qIiIXJtvEyYFtgUF5P4bWr+EvtSudVW685xcd2S89NpXOhlq+ZkP0yZSbwtYhYr2h94dy6t4XzpjN9RuNz8A5Z0Po2sht1rlvUp4E0xknasz/Lauv7uPy95F55H1Ygez80Bfh3RPwlInYqE8Cu5rr4ZtHf5frentc8IuICsl9e7pn3txfZ3N+FfV74VWTVryeSZNBaktQRf8of946IHediu8WvX+u0MDK9YZmLfasoD478kWzk3b1kHwr7pJQGpJQGpZQGAUcXspeWTykdTBYAOJVsxNTnZD+zPAl4KSLKTYPyP2QfPNeMiPXzdduRBfM+Ivu5dleoNAKo4Dyymwa9Svaz54EppYVTSkvm+2njFso+RjaKapnIpkZYg6KgST7C+3myD9SL5XUtRBbcaPZz+Bro3Ql12m51CteKXaq5TqSUptWi0XyU2lpkAc7fkQUaFiab2/8q4G95cKs9SqcIKR3xWBoULDsisqPXoxb0ofUvB6rWwmjBgo4ebxeT3YDvX8DO+WjhljxE4xcHl+UjhZtJKT2cUjqALHjXTER8Bbg0r+daYH2ym4QuVrT/CyPd6+I1rEqtHZ+V0itNOTKvOYnsC6V/k01PtFRKqW/Ra9cyRXk743ltz/lQ09fMfCqmwlRF+0LDL+Rq8WV5R1xbOLdSSl9NKa2aUtohpfTrClOqQI1fz9r6Pi6l9DTZTRq/B/yB7D3RQLLpS24CbqvwK565+jocEdsBh5O9txtPNnXTQimlxYuuZ38rZJ+bfZM0bzNoLUnzrsJcyy29MV20hbRaOJ7sZn8LAH+JiG+0kLcwumhIDdr9gMag53I1qG9u2QQYTDbyZEwe1PisJE+LgZ2U0j9SSienlLYkG025I9k0Jv2AK/NAVHH+T2mc27Qw2row2ul/yrTfFi39xLOQNpvGn0NXJf9p7pj83++mlK4vM91Exf2UUppBNjoMsoBI8dycBQ+SvQ/anJZ/5lwY5VnNtlYqW/EYzUesFaakqDSitJq2i8t2pN15cXtbUrjuzPXrRB7suTGldHBKaXWyL4p+RDZSbV3g5HZW3RCUjohFyAIeLxbNu1qcPoTsmjsbeLSkng5fj8pJKU2YS18eFo6B1qZ/GlySv0FEHAYcSDYP87dSSm+W5injNWArsmNrS+DGiFioqh43tR3ZFwbPA3ullCal5vdnqLT/O3KetqajdT9K9v5kcESsQMn1N6X0Ptk2rxURA2j5+lsP73Paavf88fCU0h9SSu+VpLfry5tWFB/bLV3ryp4LNX7NLCj8ymuv/PzYnmzbP6Txnin16kMa70vQ5v3Zmna8j5uVUro6ZXPir0g2ivkMstHv2wGHFGVv9XW4qN9t7nsLCsf9ZSmlU1JKr5T5hUNnHPuSujmD1pI07/o4fxzcQp4NOrsTKaUjgV+Tjbq5ISK2qpD1ifxx+xq0+QXwdP7vdh2tby4qPFdTWxjV8/VqK0sp/TdlNwsrfFhYmmxETqnCh8fvRMSywA75/x0d7TSyirS/p5T+28Z6lyA7nqBxDuNSre2n4tF85T5gt5ZeMDl/3KJMWkGl/VAou3JELFMhzxZkP6Etzl9V/flcmIX5K4vLdqTdeXF7W1KYD7nLrxMppXdTSr8i+xUBNN/OQpCkteBu4djdkOzmlz1peuxOJvt1xRbAqMK61HwqqJpej7pA4RjoFxFlb7IY2c0AlynJX0gbSeNz8f9SSo9V23BK6QWyffNvspuCXhfl5+5vSWH//28qc2+E/Gf/oyuU7ch52poO1Z1/UVq4bo/K65lB42s2ZMdwD7J9WPjVTLnr78f5Y9n3Ofk+Wq9cWhcq9LW9r13t8SqN+2rLchnyOe5H5f+Wu37W6jUTgJTdSPIFsunBdqbxS/NrUvkb7daN/D1LYZ7zsvszVzg/q309KttWle/jisu8llI6gcYBCcXnY6EvG0XjfQ9KFfo9g2wu71po8bjPv0BdqVyaJLXEoLUkzbsKNwlcpmTOQAAiYnNgxFzqy2Fkc3f2Bm7O2y71h/xxm1ZGZFdrQv44NiLWbilj/nPWevBJ/rhyPuK0iYjYhsofOFsKiBT/nL3ZiL+U0hNkH8AWI5suZAGym+VNKs3bRkMj4jtl+joQOCj/9y+l6VWYTjaCCLJ5XkvrX5rsZ6gtKXyYHkVj0OSpMunb0HLQpND/TSKiWRAnH0m4R4U+3E02J/ACZCNsS8v2JPtJMGQ3Tao05+8xFZ7/I8nOuf/kbdWi3Xlxe1syIX/ctrXrTq2uExGxQCs3yiqcr6XnamH+6AEt1Z9Sep5sdNxCwLH56olF6YVR1YuTXZuh/LHd7utRnXgWeDn/+4QKecbnj9PIbkoLQEQMBf5K9gXKBSmlNn+Bl1L6O9mXBh+R3ZTxT22cq7yw/9escLwcCKxYoWxHztPWFOr+VkQ0C55FxKa0HNCGxuPtELJ53QvzWZem/5jsnH4/P65LFd7nbFDhvg3fpf03Wu4shee13GvXwsBPat1gPqK1cOPpcRWClQeQfYGTKP+6XKvXzGKFL8yPJjtHIHuvOC/4a/44ttyxl18fN8n//XM1Fbb1fVwVX4SVey25nuwL0MVpfB9W3Ie+NL4+X1/F9EvVqnjc536O04JIageD1pI0j0opvU7jh/AJEfE1aAiY7E7288s2TcvQgb4ksjfHV5HdyOz2iNikJNsd+RJko9IOz38aTGRWj4izI2LnKpv9Pdno7d7A/RFxYP5TefI6B0XEdyPiQWBcBzavlh4lm990ceAPhQ9CEdEnIvYjuxnYBxXK3hsRF0TEFsVzqEbEGjQG5t6h8UN+qcKHx8IXGbWYU/IT4NJ8P/fK+7MWcBfZzX3eAy5pa6X5iNDCyPzLI2J4XnePfCT/g7T+4ecRsg9uy5H9JPWx4qBJHjCdSja3ZB+yEZPNgib5aLF78n//GhE75CPWiIgRwJ1kc1KW244ZZB/UAI6IiJ8U5jHORyL/D9lcunOAE1vYluXIfsUwNC/bNyKOoTEgd1bxSNmOtDsvbm9LUkp3kn2Ij7zOH0U2lzB53QMjYueIuJnsJle1sAbw94g4MiJWKQQk82vzrjTOE31XSbl/5I/fiojWpjx4OH8s/JqmNHj0YCvp0LHrUZfLX3cKx9GYiLgwIhYHiIjFI7spWOFLtRMLo5kjm6rgRrJfdNxL4/PRnj48SxbE+4Rs/vKro/z8suXcSxZAXBO4oOj1cJGI+BHZXNtl939HztMqXEt2LVyI7LV8s7zeHhHxTbLz6T8tlIfGUbnVHp+V5rN+lGz+8AWB/4mI5fO+9I2Ig8nmBJ8r73PaoPC8nBMRI4vO/w2A+2icHqnWfk4WaP4q2TzHq+btLhQRBwIX5Pl+n1J6pUz5mrxmlvgD2dQ7G5J9mflMfs7MCy4ie0/VB7gz8nuCRETP/DpeuKfLvSml+6uss63v47aPiMfz97dDivL3zZ/T7+arGl5L8s8Gv8v/PTMiDsqveYVfntxGNuJ5JnBalf2uRuG4Pzgi9isE3CNiuYi4kuxaXG/nqqR5QUrJxcXFxaUOFrI3rAmY2IYyG5G98Uz5Mp3sg2oi+9B6Wv73hJJyQwtlWqh7VJ5nWpm0QntDS9b3JAtMJbKfqq5fkj6AbERgofxssg/ls4rWjS0pMy1fP6pMP5Yk+6BVWt+nResScHIbn4uy21eUPr7cfq1yHx1R0rePye6onsh+Vnl4ueOAbFRh8XZ+WLLfZgBbtdCfgWRz6ab8GFm8BsfqGWTB5ZTX/UlJf7YoU3ZsNcd5mWP706L/PyCb87q1Y3hyUfkTyqT/rij9uhbqWRp4qSjvTBpHg78H7E/lc6UncGVR2S9pnC+z8FweWqbc0KIyuxYdIx8V/Z3Igm+9atXuPLy9Eylz/cjT+pHdcLRQx5y83v8UrUvAFe04zyfkecYXrRteUu9nNM7DX1j3FLBISV3DaLx+fwG8RXb9e6RMu8XXkall0jctSp8NDKjQ/3Zdjzp7oYrXqKK8p5Vs64cl+/qMFo61j4B3W1j2qOZ4IBt5Wjie/gD0qLLcOSX7/6Oivld8De/oeVrFPl09r6NQ93Qar78vkQX6Kx4XZK/1xc/BpmXyTC1KP7yFvuxSUtcnRcfo7ylzDublRrW2/bRw3WitDiq8NyGbb/j9ov7OovE9yUyyLzkKaUNbu560pc9kcyMXvy/4iCxoXPj/XqBfC3XX5DWzpMxfisr8YG5cE1rYZ83Oo1bKbUh2PSn0/z8l+/c5YMky5caXa482vo8jm1al+Powk6avp4ksCN2rpJ2+ZL9GKuT5b34sFL8mjWnL8V6UZyxlzn2yL5YeL2rjy5I2T2rp2HVxcXGptDjSWpLmYSmlv5GNXLyFLNjQi+yD4I/Ifor5ZcXCndOf2WR3h7+e7OZIdxdGyebpH5PNpbcP2YenD4H+ZAGdB8l+/n9zG9p7j2wuv+8Ct5N9UOyfJ79AFjz4NnBmuzeqxlJKFwDfonGUYy+yvp5MFmgqnXe24IA8zwPAG2Sjf8jLXgSsmVK6r4V2P6RxdNtNKaVajKD8nOxDzqnA62QfWt4nG4G0bkqp0ui5VuXH9iY0/mJgAbIgym/JgoLPVVHNgxX+LreuYl9TSu+QjQg8h2w7e5IFTn5PNsdyuVFrhbKzU0r7ALuRfYj8mOzma++QfcGzYUqpxdHoKaXryKZpuI3sg+6XZNt/ONnN45qd5x1pd17c3lbqm5FS2oVsLvfryUZu9iU7pl4m+2n3vrQ+5Uy1ppBt/2/IAr8fA4uQ7cNH8nZGpJSajFZN2TzJW5MFKz8BBpHdRLHcfL6tHdtPkV1fIJsz+eNyHe3A9ahupJROJLsx4k1koz8XJntNuRn4ekrp+BaKDyAbVVpp6VOxZNM+PEF2v4YZZK+Bl1aY8qO03NFkv1J6hux62jP/+0haeQ3vyHlaRb+eJ7vOXkZ27i5AFsQ/N2/zw1bKfwz8b/7vTJpOM1FQ7fX3BrJA7wNkx2NPsuDf/iml/VvblrktpfQqWbDzj2SvWT3JrgFXAxuklKqd2qg9bd9CNj3DpWRB9b5k+/8RsuNs25T9IqaSmrxmlihMW/I52T6YZ6SUniT7AudcsvfWC5Cdk0+Tvc/eKDW/0WZL2vo+7n6y68mVZKOvZ9L4nvke4PvAjqWviSn7JdJ2eXsP5+X6kl0nLgO+llK6qQ39blXK5gH/Otn77VfJAutf5v3cMaX0s1q2J2n+ESmlru6DJEkVRcSbZPMwbppSery1/Covn8fwHbLg2XYpmzahvXVNIPvi4ZSU0viadFBN5FNjvAaQUnIeSEnSPCciLiULnl6bUtqzq/sjSZq3ONJaklS38nmSC/PPtmU0i5r7DlnA+nWqv4mdJElSm+Vz8xcC1b9rKa8kSeUYtJYk1aX8plKH0zjlxGtd26N5Vz5qd3z+7wUpvyGZJElSreU34juHbLqe/03V36xQkqQGvbq6A5IklYqIU8nmC+ydrzLQ2g4R8SeyOc+XJvuieirQ4nzCkiRJ7RERuwG/ApYguwluAo7p0k5JkuZZjrSWJNWjRci+WH0JOBY4vWu7M88aRDYf+MfAdcA2KaXPurRHkiSpu1qY7AayvchuKvqtlNK9XdslSdK8yhsxSpIkSZIkSZLqhiOtJUmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDd6dXUH1CgiXgMWAaZ1cVckSZIkSZIkqSOGAv9JKS3f1oIGrevLIn369Bm42mqrDezqjtSb6dOnA9C/f/8u7omkWvLclrovz2+pe/Lclrovz2+pe+rKc3vKlCnMmjWrXWUNWteXaautttrASZMmdXU/6s7EiRMBGDVqVJf2Q1JteW5L3Zfnt9Q9eW5L3Zfnt9Q9deW5vd566zF58uRp7SnrnNaSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1w6C1JEmSJEmSJKlu9OrqDkiSJEmSpPnLnDlz+PDDD5k+fTqff/45KaWu7tJ8r2/fvgBMmTKli3siqZZqdW5HBAsttBD9+/dn4MCB9OjRuWOhDVpLkiRJkqS5Zs6cOfzzn/9k5syZXd0VFSkEtiR1L7U6t1NKfPbZZ3z22WfMmDGDZZddtlMD1watJUmSJEnSXPPhhx8yc+ZMevXqxaBBg+jXr1+nj9hT66ZPnw5A//79u7gnkmqpVuf2nDlzmDFjBu+++y4zZ87kww8/ZIkllqhFF8vyVUGSJEmSJM01hQDKoEGD6N+/vwFrSZoH9OjRg/79+zNo0CCg8Vreae11au2SJEmSJElFPv/8cwD69evXxT2RJLVV4dpduJZ3FoPWkiRJkiRprincdNER1pI074kIgE6/ga6vEJIkSZIkSZKkVhWC1p3NoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSfOICRMmEBFMmDChq7vSIRMnTiQiGD9+fIfq6S77o61GjhzJ1772NebMmdPVXdE87vrrryciuO+++7q6K00YtJYkSZIkSXUlor6X2m1nNFsWWmghhg4dyj777MOUKVNq15iAxiB36T5ffvnlGTt2LM8//3zF/FtssUXFeqdNm0aPHj0a8pYq91wXL20Juv/1r3/loYce4pRTTqmLG5o++eSTHH/88Wy33XYMGjSIiGDw4MGtlnvzzTfZb7/9+OpXv9pw3B955JF89NFHFcs8//zzfPvb32bJJZekd+/erLrqqpx88snMmjWrlpvUJdqzP8q55557OOaYY9hqq61YfPHFWWSRRdhmm20q5t9ll11Yd911Ofroo+vqS5BeXd0BSZIkSZKk+dnJJ5/c8Pcnn3zCk08+yR/+8Aeuu+46HnnkEYYPH96Qvssuu7Dxxhuz9NJLd0FPa2fDDTdkypQpLLHEEl3S/tprr83OO+8MZPt84sSJXHnllfz5z3/m/vvvZ+ONN26Sv1evXjz88MO8+OKLrLrqqs3qu+yyy0gp0atXL7788suK7RY/18WKn+OWpJT4yU9+wiqrrMIuu+xSVZnOds0113D++eezwAILsPrqq/Ovf/2r1TKvvPIKm266Ke+99x5jxoxh2LBhPPnkk5x//vnceeedPProoyy++OJNyvztb39j9OjRfPHFF+y2224su+yy3H///Zx66qncd9993HfffSy00EKdtZmdqj37o5KLL76Ym266id69e7PSSivx4Ycftpg/Ijj22GPZY489+NOf/sRee+1Vi03qMIPWkiRJkiRJXajcFBmHH344F110Eeedd16TUbiLLrooiy666NzrXCfp27cvw4YN67L2hw8f3mS/p5TYd999ufLKKzn++ON54IEHmuTfYYcduPHGG7nsssv45S9/2SRt9uzZXHHFFWywwQa8/fbbvPXWWxXb7eh0KPfeey9Tp07l9NNPLzuiuyuMHTuWffbZhzXWWIMFF1ywqn4deuihvPfee1xwwQUcfvjhDeuPPvpozj33XH7yk5/wm9/8pmH97Nmz2XfffZk5cyY33XQTO+20EwBz5szh29/+Ntdddx3nnnsuxx13XO03cC5o6/5oybHHHsvpp5/OsGHD+Oc//8nyyy/fapmddtqJAQMGcMkll9RN0Lrrf0MgSZIkSZKkJgo/53///febrK80h/PQoUMZOnQoM2bM4Ec/+hHLLbccCy20ECuttBJnnXUWKaWy7fz5z39miy22YPDgwSy55JJ87Wtf44wzzuDzzz9vlrfQxqeffspRRx3FsssuS58+fRg+fDg33ngjAF9++SWnn346K6+8Mr1792bFFVfkoosualZXpTmtJ02axLhx41h77bUZOHAgvXv3ZuWVV+aYY45p8zQJbRERHHrooUA23UWpNdZYg0022YQrr7ySL774oknabbfdxttvv82BBx7Yaf0r+P3vfw/AHnvs0Syt+Nh44IEHGDVqFP3792eRRRbhm9/8ZqdNNzN8+HDWWWcdFlxwwaryv/LKK9x9990MHTqUww47rEnaKaecQr9+/bjqqquYMWNGw/oHH3yQKVOmsMUWWzQErAF69OjBL37xCwB+85vfVDzOqzV27FgigldffZVzzjmHYcOG0bt3bwYPHsxRRx3Ff/7znw7VX0579kdLNtlkE9ZYYw169uxZdR969+7NzjvvzKOPPsoLL7zQpv53FoPWkiRJkiRJdebee+8FYP3116+6zBdffMG2227Lddddx3bbbccBBxzArFmzOO644zj11FOb5T/hhBPYY489mDJlCrvvvjsHHXQQKSVOOOEEtt12W/773/+WbWPrrbfm9ttvZ8yYMey999688sor7Lrrrtx3333sscce/PrXv2bUqFEccMABfPrppxx++OFce+21VW3DpZdeyp/+9CdWXXVV9t13X/7f//t/LL300pxzzjmMGDGC6dOnV70/2qoQ8Kw0UvjAAw/k/fff56abbmrW54UXXpjvfOc7nda3Qv/uv/9+Bg0axIorrlgx36233so222zDIosswiGHHMLmm2/O7bffzsiRI/n3v//dqX2sRmEU+zbbbNNsTu7+/fszYsQIZs6cyRNPPNGw/v777wfgG9/4RrP6VlhhBVZZZRVef/11Xn311Zr08aijjuJnP/sZI0eOZNy4cSyxxBKcd955jB49ms8++6wmbRS0Z390hhEjRgCN156u5vQgkiRJkiRJXah4tPF//vMfnnrqKR599FF22GEHfvjDH1Zdz9tvv83aa6/NPffcQ58+fYBsDuVVVlmFc889lxNOOIEFFlgAgMcff5wzzjiDZZddlieffJJ+/foBcPbZZ7PLLrtw66238qtf/YoTTjihWRvrrrsuEydObJg/eO+992aLLbZg9913Z8UVV+Tvf/87AwYMALLpDYYNG8aZZ55ZdnRwqeOPP56LL7642SjR3//+9xxwwAFccsklHHvssVXvk2qllLjkkksA2Gijjcrm+fa3v82RRx7JpZdeym677QbAW2+9xR133MG+++7Lwgsv3Go75aYHGTp0KGPHjm217Isvvsj777/PDjvs0GK+G2+8kbvuuoutttqqYd3xxx/PmWeeyeWXX86Pf/zjhvXPPvtswyj5ah155JENz297vPjiiwCsssoqZdNXXnll7r77bqZOndqwDdWUmTp1KlOnTm0xoF+tRx99lGeffZYhQ4YAcMYZZ7D77rtz/fXX88tf/pKTTjqpIe+NN97Is88+W3XdAwYM4Mgjj2z4vz37ozNssMEGADz00EP84Ac/6LR2qmXQWpIkSZIkqQudcsopzdatvvrqfOc736F///5tquuCCy5oCFgDLLnkkowZM4Y//OEPvPjii6y55poAXH755QCceOKJDBo0qGEEc69evTj77LO5/fbbueyyy5oFrQHOO++8Jje823zzzVl++eV57bXXOOuss5oENFdYYQVGjBjBI488wuzZs1udsqAQJCy13377cfTRR3PXXXfVJGj97LPPNgSQCzdifPbZZ+nTpw+nn3562TL9+vVjr7324re//S3Tpk1j6NChXH755cyePbvqqUHKPdcjR46sKmj9xhtvALR6E84999yzWXDzoIMO4swzz2w29cmzzz5btk8tGTt2bIeC1p988glAxbnZC+s//vjjDpXpiHHjxjU5Fnv06MEvf/lLbrzxRi6//PJmQesrr7yy6rqHDBnSJGg9t7etkkGDBgGNx1lXc3oQSZIkSZKkLpRSalg+/fRT/va3v7HUUkvx3e9+l5/85CdV17Pooouy0korNVu/7LLLAjSZE3ry5MkAjB49uln+VVZZhcGDB/Paa681BNQKBgwYUHYk61e/+lUA1ltvvWZpyyyzDF9++SXvvvtuq9vwxRdfcNFFF7HZZpsxcOBAevbsSUTQo0cP/vOf/7R4k8O2eO655zjllFM45ZRTuPjii/nwww/Ze++9efrpp9l4440rljvwwANJKfH73/+eOXPm8Pvf/5611lqLDTfcsKp2i5/rwjJx4sSqyn7wwQcALLbYYi3mKzelTLljALIAdLk+tbQMHTq0qv7Oy0aOHNls3QorrMCyyy7LtGnTmgSQJ0yY0Kb9N23atLm3IW0wcOBAgLqYQgYcaS1JkiRJklQ3+vXrx4Ybbsj111/P4MGD+cUvfsEhhxzSEHRsSaXRr716ZeGf2bNnN6wrBKMrjdpdeumleeONN/j444+bjACtNBq00Ea59EJa6Q0My9ljjz244YYbWGGFFRgzZgyDBg1qGNV93nnnlb1BZHvss88+zW5mWY11112XddddlyuuuIKNN96Y119/nQsvvLAmfWpNYQR9a3MqlzsOyh0DXaVwjJR+IVJQWF+8He0p0xFLLbVU2fWDBg3i9ddf55NPPqlZW3N72yqZNWsWQJNfanQlg9aSJEmSJEl1ZsCAAay66qpMnjyZyZMnVxW0botCoOzdd98tO3L6nXfeaZJvbnj66ae54YYb+PrXv84dd9zREGgFmDNnDr/4xS/mWl9actBBB3HIIYdwyCGH0KdPH773ve/NlXaXXHJJoHHEdS10xZzWq666KgBTp04tm/7SSy8BTed4bk+ZjvjXv/7V0Gaxwq8Fis+Ljs5pPbe3rZLCcVU4zrqaQWtJkiRJkqQ6VJjKYc6cOTWve5111mHy5MlMnDixWdD65Zdf5s0332T55Zfv9NGdpe0C7LTTTk0C1gBPPvlkw0jQrrbXXntxzDHH8Oabb/L9739/ru2jNdZYg549e/LCCy/UrM6umNN6yy23BODuu+9mzpw59OjROHvx9OnTefTRR+nbt2+TaVpGjx7N6aefzp133snxxx/fpL5XX32VqVOnMmTIEFZYYYV296vYgw8+yBZbbNGsnX/+858MHTq0yfZ3dE7r9uyPzlA4roYPH96p7VTLOa0lSZIkSZLqzI033shrr73GAgsswKabblrz+vfbbz8ATjvtNN5///2G9bNnz+aHP/whc+bMYf/99695uy0pzJVcOsfze++9x2GHHTZX+9KS/v37c+edd3LDDTdw2mmnzbV2F110UYYPH87//u//1iyA3xVzWq+44opss802TJs2jYsvvrhJ2sknn8yMGTPYe++96devX8P6kSNHstpqq/HQQw9x8803N6yfM2dOw405DznkECKiSX1Dhw4lIto8j/T555/P66+/3qSdH/3oR8yZM4d99923Sd6Ozmndnv0BWZC5ll9gPPHEE0BjEL2rOdJakiRJkiSpC40fP77h7xkzZvD8889zxx13APDzn/+84vy6HbHpppvy4x//mF/84hesueaa7LTTTvTr14/77ruPv//972y22Wb86Ec/qnm7Ldlggw0YMWIE119/PZtuuimbbbYZ//rXv7jjjjtYddVVG272WA8222yzLml31113ZdKkSdx///1885vf7JI+lHrhhRc488wzm6z76KOPGDt2bMP/v/rVr1hiiSUa/r/kkkvYdNNNOeKII7jvvvtYbbXV+Nvf/sYDDzzAKquswumnn96kvp49e3LFFVcwevRodtttN3bbbTeWW2457rvvPp5++mlGjBjBUUcd1axvhV8plI7cb82IESMYPnw4e+yxB4suuih33XUXzz33HOuttx4//vGP21RXNdq6PwBWW201ILu5Z7FHHnmEyy67DIBPP/0UgFdeeaXJ81FuPve7776bAQMGlL05a1cwaC1JkiRJktSFiqdn6NmzJ1/5ylfYcccd+cEPfsDWW2/dae2eddZZrLPOOlx00UX86U9/4osvvmDFFVfktNNO45hjjmHBBRfstLbL6dmzJzfffDMnnngit99+OxdccAHLLLMMBxxwACeeeCKrr776XO1PPdp///0ZP348f/jDH+omaP3uu+82mx5j5syZTdaNHz++SdB6xRVX5Omnn+anP/0pd955J7fffjtLL70048aN4+STT2axxRZr1s5GG23EU089xcknn8zdd9/N9OnTGTJkCD/96U857rjjGm7YWfDRRx/x1ltvMWLECAYPHtymbTr33HO54YYbuPTSS5k2bRqLL74448aN49RTT6V3795tqqsa7dkflbz88svNno/333+/ybrSoPXUqVN54oknGDduHH379u3QttRKlEbj1XUiYtK666677qRJk7q6K3Wn8NOgUaNGdWk/JNWW57bUfXl+S92T57ZqYcqUKUDjKEHVh+nTpwPZ1BeqbwcffDBXXnkl06ZNY9CgQV3dnbp18803M2bMGG677Ta23377qsqMHTuWK6+8ktdee63D06DUi2rO7WOOOYaLLrqIKVOmVDUveLXX8fXWW4/JkydPTimt14YuA85pLUmSJEmSJM0zTj31VBZccMGyU0ao0YMPPsjw4cOrDljPr9555x1+/etfc/jhh9fsRpa14PQgkiRJkiRJ0jxiqaWW4o9//CP/+Mc/mDNnDj16OCa1nLPPPruruzBPmDZtGsceeyzjxo3r6q40YdBakiRJbVJyU/ayCp8Rqrn5uLPVSZIktc1OO+3ETjvt1NXdUDewySabsMkmm3R1N5rxqxhJkiRJkiRJ870JEyaQUuo281nPywxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Y1eXd0BSZKk+UlE7epKqXZ1SZIkSVK9cKS1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLrhnNaSJEmSJKm+XFPDm0B0hr3q/8YSY8eO5corr+S1115j6NChXd0dteCBBx5g9OjRXHvttXz7299uWF943qZNm9Y1HStjwoQJ7LvvvlxxxRWMHTu27uqrd5MmTWL99dfn0ksv5YADDujq7tQ1R1pLkiRJkiR1gYhosvTs2ZMllliC0aNHc80113R19+YJQ4cObbIPe/TowYABA9h00025+OKL+fLLLyvmv//++yvWu++++zbkGz9+fJO08ePHN3vuipe2fEkwZ84cjjrqKNZee2123333tmy6amzKlCmcfPLJjBkzhuWWW67h+Sw9hkp9+OGHHHnkkQwdOpSFFlqIr371q+y33368+eabzfKut9567Lzzzpx00kl8+umnnbUp3YIjrSVJkiRJkrrQySefDMAXX3zBCy+8wE033cQDDzzA008/zTnnnNOuOs844wyOO+44lllmmVp2tW6NGzeOAQMGMHv2bF577TWuu+46Hn/8ce677z6uv/76Zvl79erFZZddxujRo5ul/ec//+HPf/4zvXr1ajFgOXLkSEaNGtVs/YABA6ru95/+9Ceee+45rr76aiLq/BcG3dxdd93FqaeeSs+ePVl55ZXp3bs3n332WYtlPvjgAzbddFOmTp3K6NGj2XPPPXnhhRe44ooruO2223j88cdZYYUVmpQ5/vjj2Wijjbjgggs44YQTOnOT5mkGrSVJkiRJkrpQ6Uje++67j6233przzjuPI444ol3Teyy99NIsvfTStengPKAw0rXg+OOPZ4MNNuCGG27gwQcfZOTIkU3y77DDDlx//fV88MEHLL744k3Srr76ambOnMkuu+zCDTfcULHNUaNGNXvu2uriiy9mkUUWYZdddulQPeq47bbbjk022YS11lqLPn36MHToUF5//fUWy5xwwglMnTqVo48+mrPPPrth/QUXXMC4ceM49NBDufPOO5uU2XDDDRk2bBi//e1vOe644+jRw4kwynGvSJIkSZIk1ZGtttqKYcOGkVLiqaeealg/adIkdt11V5ZcckkWWmghhgwZwqGHHso777zTrI6xY8cSEc3mQ7755pvZaqutWHrppRumMhg5ciSXXnppk3yvvvoqBx10ECuttBJ9+vRh4MCBfO1rX+OQQw7hgw8+aJL3888/58wzz+RrX/saffv2ZZFFFmHzzTfnz3/+c7N+TZs2jYhg7NixTJs2jT333JMllliC3r17s/7663Prrbd2YM81WmONNRpGQT/55JPN0g888EA+//xzrrrqqmZpl156Kcsuuyzf+MY3atKXSl544QUee+wxdtppJ/r06VNVmU8++YRf/vKXjB49msGDB7Pgggvyla98hZ122onHH3+8bJmIYNSoUfzrX/9iv/32Y6mllqJfv35suummPPzwwwDMmDGDH/3oRwwZMoSFFlqINdZYg7/85S8t9uW2225j0003pV+/fiy22GLstttuvPTSS2Xzvvzyy+y+++4stthiDW3fdtttFet+4IEHOOigg1h99dVZZJFF6NOnD2uuuSannHJKq6Of22vVVVdlo402qvq5+PTTT7nqqqvo169fsy8vfvCDHzBkyBDuuusuXn311WZl99xzT9544w3uueeeWnS9WzJoLUmSJEmSVGdSym72WJgy4tZbb2XTTTfllltu4etf/zpHH300q666Kr/+9a9Zf/31ee2111qt83e/+x1jxozh+eefZ8cdd+SYY45h++23Z9asWfzxj39syPfOO++wwQYbcMUVV7DGGmtwxBFHsPfee7P88stz1VVXNQmS//e//2Xbbbfl+OOP58svv+Swww5j7733ZurUqeyxxx4Vpz94/fXX2XDDDZk2bRp77703e+yxB3//+98ZM2YMDzzwQEd2XYPSfVhs6623ZujQoVx22WVN1k+aNIlnnnmG/fbbr9NHwN57770AbLbZZlWXmTJlCj/5yU/o0aMH3/zmNzn66KPZeuutuf/++9liiy2ajeot+PjjjxkxYgTPPPMM3/nOd9h11115+umn2XbbbXnuuefYaqutuOmmm9hhhx3YZ599eOONN9hjjz144oknytZ3/fXXs/POOzN48GDGjRvHJptswnXXXcfGG2/Miy++2CTvSy+9xMYbb8xf//pXNtlkE8aNG8fgwYPZeeedy07dAnDWWWdx9913M3z4cA4++GAOOOAAFlxwQcaPH892223H7Nmzq95nneWJJ55g1qxZjBgxgv79+zdJ69GjB9tuuy1A2eN5xIgRAAatW+D0IJIkSZIkSXXk3nvv5cUXXyQi2GCDDfj000/ZZ599+PLLL5k4cSKbb755Q96zzjqL4447joMPPpi77767xXp/+9vfsuCCC/Lcc8+x5JJLNkkrHpH917/+lQ8//JDzzjuPcePGNck3Y8aMJsHcs88+mwcffJDtttuOm2++mV69slDTySefzIYbbsgZZ5zBDjvswKabbtqknokTJzJ+/PiG+bwB9tprL77xjW/wy1/+ki233LK6nVXBP/7xDx588EEANtpoo2bpEcH+++/PSSedxOOPP84mm2wCZKOse/TowX777dfq/ixsQ6mxY8dWNaXLI488AsD666/fat6C1VZbjbfffpsllliiyfo333yTDTfckKOOOqrsCPHnnnuOgw8+mEsuuaTh+dt66635/ve/z5ZbbsmIESOYOHEivXv3BmDvvfdmiy224Kyzzio7Rcott9zCLbfcwg477NCw7vzzz+fII4/k0EMP5b777mtYf9hhh/HBBx80O55uuukmdt5557Lbeckll7D88ss3+8LhpJNO4rTTTuOvf/0re+yxR8P6adOmMWHChAp7rbxqn6dKCsH5VVZZpWz6yiuvDMDUqVObpW2wwQYAPPTQQ+1uv7szaC1JkiRJktSFCoHPL774ghdffJEbb7yRlBJHHXUUQ4YM4eqrr+bDDz/kO9/5TpOANcAxxxzDb37zG+655x7eeOMNlltuuRbb6tWrFwsssECz9aXzOgNlp0no169fk/8vv/xyIoJzzjmnIWANsOSSS3LSSSdxwAEHcNlllzULWg8ZMoQTTzyxybptt92W5ZZbrux0Hq0577zzmtyI8frrr2fWrFnssssuzfZZwb777sv48eO59NJL2WSTTZgxYwbXXHNNQz9a8+CDDzYExouNGjWqqmDoG2+8AdCmuccXXXTRsusHDx7MbrvtxoUXXlj2OOjbty+//OUvm3zhsNdee7Hffvvx0Ucfcf755zcErAE233xzhg4dyrPPPlu2vdGjRzcJWEM2JcaFF17I/fffz+uvv86QIUN48803ueeee1h++eX5wQ9+0CT/mDFjGDlyZNl9WHrzwoKjjjqK0047jbvuuqtZ0PqUU04pW6aSap+nSj755BOg8nNSWP/xxx+XTevdu3fDMaDmDFpLkiRJkiR1oUKwLSIYMGAAm2++Ofvvvz/f+973AJg8eTKQBQpL9erViy222IJp06bxzDPPtBhs/e53v8sxxxzD6quvzp577snIkSMZMWIEX/nKV5rk22mnnTjhhBM47LDDuOuuu9h2220ZMWIEq6++epORr9OnT+fll19mmWWWYdiwYc3aK/T3mWeeaZY2fPhwevbs2Wz9sssuW3Fu5pacf/75QLYPF154YdZaay2+973vccghh1Qss8wyy7D99tvz5z//mfPPP58///nPTJ8+nQMPPLCqNk8++eQO3YixMDf4Yost1qZyjz76KOeffz6PP/447733Hv/973+bpL/11lvNjoNVVlml2RQWPXv2ZKmllmLGjBllg8TLLLMMf/vb38r2ofTGloX6NttsM1555RWeeeYZhgwZ0vDcb7bZZmWf71GjRpUNWs+YMYPzzz+fG264galTpzJ9+vSG6V4K21haT3H6vGDgwIH861//6upu1C2D1pIkSZIkSV2otWBbYURnpRG5hfXlRnQWO/roo1liiSW45JJLuOCCCzjvvPOICEaOHMn48eNZd911gWwU9JNPPsn48eO58847G+YdXnbZZfnhD3/IEUcc0eF+DRgwoGyZXr16MWfOnBa3o5zXXnutXaNmDzzwQG655RauueYarrjiCgYNGsSOO+7Y5nraozCS/bPPPqv65n833HADu+22G71792brrbdmxRVXpF+/fvTo0YOJEyfy4IMP8vnnnzcrV2k0cK9evVpM+/LLL8umLbXUUmXXDxo0CGg8NgqPreUv9sUXXzB69GiefPJJ1lxzTfbYYw++8pWvNPxC4JRTTim7jXNbYb8VtrFUYX2lY33WrFlVP+/zI4PWkiRJkiRJdawQHHv33XfLphdujFgp+Fjs+9//Pt///vf5+OOPeeyxx7jhhhu4/PLL2WWXXZg0aVLDaNzVVluNa6+9li+//JLnnnuOe++9lwsvvJBx48bRr18/9t9//5r2q6tsv/32LLPMMpx22mm8+eabHH/88U2mOelMhXnFP/jgg6pHW5900kksuOCCPP3006y22mpN0g4++OCyo5Y7Q6URwoVjofCcFx5by1/spptu4sknn2Ts2LFcccUVTdLeeeedstOAdMWc1quuuipQfs5qyG5ACeXnvJ4zZw4ff/wxyy+/fLvb7+4MWkuSJEmSJNWxddZZB8hu/Lf//vs3Sfvyyy95+OGHARpGSldjwIABbL/99my//fbMmTOHyy+/nEcffbRZEK1Xr16st956rLfeemy66aZsscUW3Hjjjey///7079+fFVdckVdffZWXXnqp4cZzBQ888ECb+zW39ezZk/3224+f/exnRAQHHHDAXGt7rbXW4p577uGFF15gpZVWqqrMyy+/zBprrNEsYD1nzpyGGzvODeWC47Nnz27oQ+GYLTw+8sgjzJ49u9kUIRMnTmxWz8svvwzAt771raraha6Z03rjjTemT58+PProo0yfPr3J9Ctz5sxpuJFnuZuKvvjii6SUGD58eLvb7+56tJ5FkiRJkiRJXWXnnXdm4MCB/M///A9PPPFEk7TzzjuP1157ja9//eut3jzwgQceKDsVyXvvvQc0TlcxadKkslMeFEbL9u3bt2HdfvvtR0qJH/3oR8yePbth/b///W9+9rOfNeSpZ0cccQQ33HADd911V8UbAHaGUaNGATR7TlsydOhQXnrpJd5+++2GdSklxo8fz/PPP1/rLlZ0//33c+uttzZZd9FFF/HKK6+w5ZZbMmTIECC7QeTWW2/Na6+9xkUXXdQk/0033VQ2CF0IJJcGtF999VWOPfbYsv0pzGndlqWw/9tr4YUXZu+992bGjBnN5ja/6KKLmDZtGttuu23ZY6rwnJcLaCvjSGtJkiRJkqQ6tvDCC3P55Zez++67M3LkSHbffXeWW245Jk2axN13382gQYP47W9/22o9u+yyCwsvvDAbb7wxQ4cOJaXEww8/zFNPPcU666zTEEC76qqr+O1vf8tmm23GiiuuyGKLLcYrr7zCLbfcwkILLcSRRx7ZUOcPf/hD7rjjDm666SbWXntttt9+e2bOnMlf/vIX3nvvPX784x+z2WabddauqYkllliCnXfeea63O3r0aAYMGMBdd93FaaedVlWZo446ikMOOYR11lmHXXfdlQUWWIBHH32U559/nh133JFbbrmlk3ud2XHHHdlll13YZZddWGmllXj22We54447GDhwIJdcckmTvBdffDGbbLIJRx55JHfffTdrr702L7/8MjfccEPZPu+4446stNJKnHPOOfzf//0f66yzDm+88Qa33nor3/zmN3njjTc6ZZv+/e9/88Mf/rDJ/wD7779/ww1IjzvuuCY3Hf35z3/OxIkTOeecc3j22WfZcMMNmTJlCjfddBNLLrkkF198cdm27r77bnr27MmYMWM6ZVu6A4PWkiRJkiSpvuzV8o0J50djxozh0Ucf5ec//zl33XUXn3zyCYMGDeKQQw7hpJNO4qtf/WqrdZx55pncddddTJ48mdtvv53evXszZMgQzjrrLL73ve813OjuO9/5Dp9//jmPPfYYkyZNYtasWSyzzDLsueeeHHPMMay55poNdS644ILcc889nHPOOVxzzTVceOGF9OrVi7XXXpvzzjuP73znO522T+Z1ffv2ZezYsZx33nlMmTKl2ZQf5Rx88MEstNBCnHfeeVx55ZX06dOHzTffnCuuuILrrrturgWtv/Wtb3HQQQdx+umnc9ttt7HAAgvwrW99izPOOKPZHM4rr7wyTzzxBMcddxz33nsvEydOZK211uLGG2/k/fffb9bnfv36cf/993PccccxceJEHn74YVZYYQVOOukkjj76aK699tpO2aZPP/2UK6+8stn6P/zhDw1/jx07tknQevHFF+fxxx/nlFNO4cYbb+Thhx9m8cUXZ9999+XUU09l8ODBzer75JNPuPHGG9lhhx1YdtllO2VbuoNo7Q61mnsiYtK666677qRJk7q6K3Wn8JOQjv50Q1J98dzW/CgfpFETXfU2rpptOPvsiQAcc8yoVvP6dlSad/jarVqYMmUKQFUBOs0906dPB2gyL68632uvvcawYcM45JBDOP/887u6O5oLLrzwQo444ggefvjhufIrhM44t6u9jq+33npMnjx5ckppvba24ZzWkiRJkiRJUhdYfvnlGTduHL/73e946623uro76mSzZs3ijDPOYNddd637aXO6mtODSJIkSZIkSV3kxBNPpF+/fkybNo1lllmmq7ujTjRt2jQOOuggxo4d29VdqXsGrSVJkiRJkqQussgii3DyySd3dTc0F6y22mqMHz++q7sxT3B6EEmSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEmtSinNlXYMWkuSJEmSpLkmIgCYM2dOF/dEktRWhaB14VreWQxaS5IkSZKkuWahhRYCYMaMGV3cE0lSWxWu3YVreWcxaC1JkiRJkuaa/v37A/Duu+8yffp05syZM9d+bi5JaruUEnPmzGH69Om8++67QOO1vLP06tTaJUmS1Gbp6ip/andNlRXu1TWBgHWHTiZdvWXrGet8OyRJtTVw4EBmzJjBzJkzefPNN7u6O8rNnj0bgJ49e3ZxTyTVUmec23379mXgwIE1q68cg9aSJEmSJGmu6dGjB8suuywffvgh06dP5/PPP3ekdR2YOXMm0PmjJyXNXbU6tyOChRZaiP79+zNw4EB69OjcCTwMWkuSJEmSpLmqR48eLLHEEiyxxBJd3RXlJk6cCMCGG27YtR2RVFPz6rntnNaSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6sY8GbSOiMERcXlEvB0Rn0fEtIg4LyIWa0MdW0fE2RFxX0R8EBEpIh5pIf8yEXF4RNyRt/d5Xu6eiPhWbbZMkiRJkiRJkuZvvbq6A20VESsCjwFLAjcBLwAbAuOAb0TEiJTSB1VUdRgwBvgMeBkY2Er+w4FjgdeAB4B3gSHAt4CvR8S5KaWj275FkiRJkiRJkqSCeS5oDVxCFrA+IqV0YWFlRJwDHAWcDhxSRT1nAT8hC3ovSxaMbsmTwKiU0oPFKyNiNeAJ4KiIuDqlNKnaDZEkSZIkSZIkNTVPTQ+Sj7LeBpgGXFySfDIwA9g7Ivq1VldK6fGU0j9SSrOraTuldH1pwDpfPwW4Nv93VDV1SZIkSZIkSZLKm6eC1sCW+ePdKaU5xQkppenAo0BfYOO53K8v8scv53K7kiRJkiRJktStzGvTg6yaP06tkP4S2UjsVYD75kaHImIRYFcgAXdXWabSFCLDpk+fzsSJE2vUu+5j+vTpAO4bqZvx3Nb86OyzW88zsXcVmdqixudYNdswePB0pvcYXNtt8VohdTlfu6Xuy/Nb6p668twutN0e89pI60Xzx08qpBfWD+j8rkBEBHAZsBTw63yqEEmSJEmSJElSO81rI63rzdnA7sDDwNHVFkoprVdufURM6t+//7qjRo2qTe+6kcK3Qe4bqXvx3Nb8aMstW8+Trq4iU1uMSjWtrpptOPvsiaw79CVGfXZM7Rqu8XZE1K6uVNuuSXXL126p+/L8lrqnrjy3+/fv3+6y89pI68JI6kUrpBfWf9zZHYmIXwBHAQ8B26eUPu/sNiVJkiRJkiSpu5vXRlq/mD+uUiF95fyx0pzXNRER5wJHAg8AO6SUZnZme5IkSZIkSZI0v5jXRlo/kD9uExFN+h4R/YERwEzgic5oPDIXkwWs7wG+acBakiRJkiRJkmpnngpap5ReAe4GhgKHlSSfAvQDrkopzSisjIhhETGso23nN138HXAocAewU0ppVkfrlSRJkiRJkiQ1mtemB4EsaPwYcEFEbAVMATYCtiSbFuQnJfmn5I9NbrUTEZsBB+T/Lpw/rhwREwp5Ukpji4r8NM8/C3gWOC6a373n2ZTSjW3cHkmSJEmSJElSbp4LWqeUXomI9YFTgW8A2wPvAOcDp6SUPqqyqpWAfUrWLVmybmzR38vnj32A4yvUeSVwY5XtS5IkSZIkSZJKzHNBa4CU0j+BfavM22w4dL5+AjChDW2OpWkQW5IkSZIkSZJUY/PUnNaSJEmSJEmSpO7NoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Y1eXd0BSZKkakTUtr6UalufJEmSJKk2HGktSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkutGrqzsgSZIk1at0dVSX8ZoqK9wrtbsvkiRJ0vzCkdaSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1o1dXd0CSJKmW0tVRXcZrqqxwr9TuvkiSJEmS2s6R1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXVjngxaR8TgiLg8It6OiM8jYlpEnBcRi7Whjq0j4uyIuC8iPoiIFBGPVFFu9Yj4c0S8FxGfRcSLEXFKRPTp2FZJkiRJkiRJknp1dQfaKiJWBB4DlgRuAl4ANgTGAd+IiBEppQ+qqOowYAzwGfAyMLCKtjcC7gcWAP4K/BMYDfwU2Coitkopfd7mjZIkSZIkSZIkAfPmSOtLyALWR6SUdk4pHZdSGg2cC6wKnF5lPWcBawILAzu2ljkiegJXAH2B3VJKe6WUjgU2Aq4DRgBHtXVjJEmSJEmSJEmN5qmgdT7KehtgGnBxSfLJwAxg74jo11pdKaXHU0r/SCnNrrL5kcBqwEMppZuL6pkD/Dj/95CIiCrrkyRJkiRJkiSVmKeC1sCW+ePdebC4QUppOvAo2UjojTuh7dH5452lCSmlV4GpwBBghU5oW5IkSZIkSZLmC/PanNar5o9TK6S/RDYSexXgvi5oe5V8eaWliiJiUoWkYdOnT2fixInt6mB3Nn36dAD3jdTNeG6rLc4+u7p8E3tXmbFaNT4+q9mO7rANgwdPZ3qPwbXdFp8Lqcv52i11X57fUvfUled2oe32mNdGWi+aP35SIb2wfkA3a1uSJEmSJEmS5gvz2kjrbiGltF659RExqX///uuOGjVqLveo/hW+DXLfSN2L57baYsstW88DkK6uMmO1RqWaVlfNdnSHbTj77ImsO/QlRn12TO0a9rmQupyv3VL35fktdU9deW7379+/3WXntZHWhdHMi1ZIL6z/uJu1LUmSJEmSJEnzhXktaP1i/rhKhfSV88dK807Pq21LkiRJkiRJ0nxhXgtaP5A/bhMRTfoeEf2BEcBM4IlOaPv+/PEbpQkRsQJZMPt14NVOaFuSJEmSJEmS5gvzVNA6pfQKcDcwFDisJPkUoB9wVUppRmFlRAyLiGE1aP5BYAqwRUTsVFR/D+Cs/N/fpJScqFCSJEmSJEmS2mlevBHjocBjwAURsRVZIHkjYEuyqTl+UpJ/Sv4YxSsjYjPggPzfhfPHlSNiQiFPSmls0d+zI2JfshHXf42IvwJvAFsB6wOPAud2cNskSZIkSZIkab42zwWtU0qvRMT6wKlkU3VsD7wDnA+cklL6qMqqVgL2KVm3ZMm6sSVt/y0iNiAb1b0N0J9sSpBTgTNTSp+3bWskSZKk9otoPU9b+JtBSZIk1YN5LmgNkFL6J7BvlXnLvpVPKU0AJrSj7eeB3dtaTpIkSZIkSZLUunlqTmtJkiRJkiRJUvdm0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3ejV1R2QJEmS1LnS1VFdxmuqrHCv1O6+SJIkSa1xpLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqhkFrSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXWjV1d3QJIk1Ylrorb17ZVqW58kSZIkab7gSGtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakqT5QETriyRJkiRJ9cCgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS60atWFUXE1sDWwBbAcsASwCzgPeBZ4H7g5pTSW7VqU5IkSZIkSZLUvXQoaB0RfYEjgIPJAtWRJ31GFqzuA6wArAjsCpwfEbcAv0opPd6RtiVJkiRJkiRJ3U+7pweJiP2Al4Cfk42oPoVspPWAlFLflNLglNLiZIHx1YH9gOuA7YBHIuLaiFiuoxsgSZIkSZIkSeo+OjLS+jLgRuCMlNJTlTKllBLwQr5MiIhFgH2A44CxwKkd6IMkSZIkSZIkqRvpSNB6/ZTS5LYWSin9B7gwIi4FhnagfUmSJEmSJElSN9PuoHV7AtYl5T8jG30tSZIkSZIkSRLQgTmtS0XEWlXm279WbUqSJEmSJEmSupeaBa2B2yNicEsZImJv4DcdbSgiBkfE5RHxdkR8HhHTIuK8iFisjfUMzMtNy+t5O6+34nZExDcj4u6IeDMiZkXEqxHxl4jYpKPbJUmSJEmSJEnzu1oGrfsDd0bEgHKJEbE7cDnwUkcaiYgVgUnAvsCTwLnAq8A44PGIWLzKehYHHs/LvZLX82Re76SIWKFMmbOAW4F1gTuB84HJwBjg0Yj4Xke2TZIkSZIkSZLmd7UMWu8CrATcGBELFidExBjgamAasFUH27kEWBI4IqW0c0rpuJTSaLKg86rA6VXW83NgFeCclNJWeT07kwWxl8zbKd6GQcAPgX8Bq6eUDsjL7AZsCwRwage3TZIkSZIkSZLmazULWqeU7gf2BzYH/lhYHxHbAdcCbwOjU0rvtLeNfJT1NmTB74tLkk8GZgB7R0S/VupZGNg7zz++JPki4HVg25LR1kPI9tffUkrvFRdIKT0ATAe+0obNkSRJkiRJkiSVqOVIa1JKVwMnALtFxLkRsRVwHfBvsoD1PzvYxJb5490ppTklbU8HHgX6Ahu3Us/GQB/g0bxccT1zgLtK2oNsWpP/AhtGxBLFZSJiC7LpUe6tflMkSZIkSZIkSaUipVT7SiMuAg4FvgA+BkamlF6oQb2/JJui44cppbMrtHsYcGhK6dct1HMY2Yjqi1JKh5dJ/yHwS+AXKaVji9YfCZxDFoS/EfgAWBHYCXgI+F7pKOwK7U+qkDRs5ZVX7vu73/2utSrmO9OnZ98t9O/fv4t7IqmWPLfnnsmTW8+z7tAqMrXFwHVrWl012wDdYzu6wzYMHjydPgvOov+cN2vXsM9FM93lvNC8w9duqfvy/Ja6p648tw866CBeeumlySml9dpatldndAg4HPgq2VQhW9UiYJ1bNH/8pEJ6Yf2AzqgnpXReREwju6HkgUVJLwMTqglYS5IkSZIkSZIqa3fQOiLmANUM034uIor/TymlzgqWd6qI+DHZDRwvIBup/S4wDDgDuDoihqeUftxaPZW+XYiISf3791931KhRtet0NzFx4kQA3DdS9+K5PfdsuWXredLVVWRqi1G1/TVXNdsA3WM7usM2nH32RNYd+hKjPjumdg37XDTTXc4LzTt87Za6L89vqXvqynO7I6O7OxI8fojqgta1VBgBvWiF9ML6j2tdT0SMAs4CbkgpHV2Ud3JE7AJMBY6JiN+klF5tpX1JkiRJkiRJUhntDlqnlEbVsB/VejF/XKVC+sr549ROqGeH/PGB0swppZkR8SSwC7AOYNBakiRJkiRJktqhR1d3oI0KAeNtIqJJ3yOiPzACmAk80Uo9TwCzgBF5ueJ6egDblLQHsFD++JUKdRbW/7eVtiVJkiRJkiRJFcxTQeuU0ivA3cBQ4LCS5FOAfsBVKaUZhZURMSwihpXU8ylwVZ5/fEk9P8jrv6tkmo+H88eDImKZ4gIRsR1ZwPwz4LG2bpckSZIkSZIkKVPzGyJGxHLA0JTSQ+X+r4FDyQLDF0TEVsAUYCNgS7LpPH5Skn9KoWsl608ARgFHR8Rw4ElgNWAM8B7Ng+J/Be4Fvg5MiYgbyG7EuBrZ1CEBHJdS+qBjmydJkiRJkiRJ86/OGGm9L02n1Sj9v0Py0dbrAxPIgtXHACsC5wMbVxs0zvNtAlwArJTXsxFwBbBe3k5x/jnA9sBRwPNk81cfA2wM3A5sm1I6v4ObJ0mSJEmSJEnztZqPtJ4bUkr/JAuGV5O3dIR1cdqHwLh8qaauL4Dz8kWSJEmSJEmSVGPz1JzWkiRJkiRJkqTuzaC1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLph0FqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJEmqGwatJUmSJEmSJEl1ozOC1pEvlf6XJEmSJEmSJKmszghaXwFs2cL/kiRJkiRJkiSV1avWFaaUXgder/S/JEmSJEmSJEmVdGikdUTsUKuOSJIkSZIkSZLU0elBbo6ISyKiT016I0mSJEmSJEmar3U0aD0ZOASYHBHr1qA/kiRJkiRJkqT5WEeD1hsDPwdWAh6PiBMiIjreLUmSJEmSJEnS/KhDQeuU0pcppROBkcCbwM+AByNiSC06J0mSJEmSJEmav/SqRSUppcciYi3gAmBf4LmI+DUwq3z29LNatCtJkiRJkiRJ6l5qErQGSCnNAPaPiC+BA4EfA8VThaT8/0Q2IluSJEmSJEmSpCZqFrSOiIWBi4C9gU+BSyg/0lqSJEmSJEmSpLJqErSOiE2Bq4DlgceBvVNKr9aibkmSJEmSJEnS/KNDN2KMiJ4RcRrwILAscDKwuQFrSZIkSZIkSVJ7dHSk9ePAesDLwPdSSk91vEuSJEmS5icRreepVkq1q0uSJEldo0MjrYH1gUuBdQxYS5IkSZIkSZI6qqMjrceklG6pSU8kSZIkSZIkSfO9Do20NmAtSZIkSZIkSaqldgetI+KHEdG7A+XXiYjt2ltekiRJkiRJktT9dGSk9enAKxFxbER8tZoCkdk2Im4AngbW7kD7kiRJkiRJkqRupiNzWn8NOAc4AzgtIh4DHiELRr8DfAT0BhYHhgEbA1sBg4APgB8Av+1A+5IkSZIkSZKkbqbdQeuU0lRgh4jYFDgM2BXYHEhlskf++CJwFnBFSml6e9uWJEmSJEmSJHVPHRlpDUBK6THgsYg4BNgC2AxYjmyE9SzgPeB/gYkppX90tD1JkiRJ8590dbSeCeCaKivcq9xYG0mSJNWDDgetC/KR07fliyRJkiRJkiRJbdaRGzFKkiRJkiRJklRTHQ5aR8TyEfH7iPi/iPjfiPhdRAytQd8kSZIkSZIkSfOZDk0PEhHLAE8AS9B4s8U1gZ0iYr2U0lsd7J8kSZIkSZIkaT7S0ZHWxwNfAe4H9gD2BB4AlszTJEmSJEmSJEmqWkdvxLg1MBX4RkppNkBEXAc8D2zTwbolSZIkSZIkSfOZjo60Xha4uxCwBsj/vitPkyRJkiRJkiSpah0NWvcG/l1m/QfAgh2sW5IkSZIkSZI0n+lo0FqSJEmSJEmSpJrp6JzWAKMiotk6gIg4CShNTCmln9WgXUmSJEmSJElSN1OToHW+lHNK0d+JLICdAIPWkiRJkiRJkqRmOhq0PqX1LJIkSZIkSZIkVadDQeuUkkFrSZIkSZIkSVLNeCNGSZIkSZIkSVLdMGgtSZIkSZIkSaobBq0lSZIkSZIkSXXDoLUkSZIkSZIkqW4YtJYkSZIkSZIk1Q2D1pIkSZIkSZKkumHQWpIkSZIkSZJUNwxaS5IkSZIkSZLqxlwLWkfEchHx1bnVniRJkiRJkiRp3jM3R1pPA/4ZEQ9GxLZzsV1JkiRJkiRJ0jxibgat3wDeBEYAt0fE03OxbUmSJEmSJEnSPKDX3GoopTQUICIGAFvkiyRJkiRJkiRJDeZa0LogpfQxcHO+SJIkSZIkSZLUYG5ODyJJkiRJkiRJUosMWkuSJEmSJEmS6kbNpgeJiK2Brcnmql4OWAKYBbwHPAvcD9ycUnqrVm1KkiRJkiRJkrqXDgWtI6IvcARwMFmgOvKkz8iC1X2AFYAVgV2B8yPiFuBXKaXHO9K2JEmSJEmSJKn7aff0IBGxH/AS8HOyEdWnkI20HpBS6ptSGpxSWpwsML46sB9wHbAd8EhEXBsRy3V0AyRJkiRJkiRJ3UdHRlpfBtwInJFSeqpSppRSAl7IlwkRsQiwD3AcMBY4tQN9kCRJkiRJkiR1Ix0JWq+fUprc1kIppf8AF0bEpcDQDrQvSZIkSZIkSepm2h20bk/AuqT8Z2SjryVJkiRJkiRJAjowp3WpiFirynz716pNSZIkSZIkSVL3UrOgNXB7RAxuKUNE7A38poZtSpIkSZIkSZK6kVoGrfsDd0bEgHKJEbE7cDnwUg3blCRJkiRJkiR1I7UMWu8CrATcGBELFidExBjgamAasFUN25QkSZIkSZIkdSM1C1qnlO4H9gc2B/5YWB8R2wHXAm8Do1NK79SqTUmSJEmSJElS99KrlpWllK7O57U+IyLOBW4FrgP+TRaw/mct25MkSZIkSZIkdS81DVoDpJTOiohlgXHAocDHwNdTSq/Wui1JkiRJkiRJUvdS86B17nDgq2RThWyVUnqhk9qRJEmSJEmSJHUj7Q5aR8QcIFWR9bmIKP4/pZQ6K1guSZIkSZIkSZqHdSR4/BDVBa0lSZIkSZIkSapKu4PWKaVRNeyHJEmSJEmSJEn06OoOSJIkSZIkSZJUYNBakiRJkiRJklQ3ah60jojlImKLSv9LkiRJkiRJklRJZ4y03hd4oIX/JUmSJEmSJEkqy+lBJEmSJEmSJEl1w6C1JEmSJEmSJKluGLSWJEmSJEmSJNUNg9aSJEmSJEmSpLrRq6s7IElSt3BN1La+vVJt65MkSZIkaR7hSGtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVjc4IWke+VPpfkiRJkiRJkqSyOiNofQWwZQv/S5IkSZIkSZJUVq9aV5hSeh14vdL/kiRJkiRJkiRV4pzWkiRJkiRJkqS60aGgdURs18b8/SLidx1pU5IkSZIkSZLUfXV0pPVtEXFRRPRuLWNEbAY8B+zfwTaJiMERcXlEvB0Rn0fEtIg4LyIWa2M9A/Ny0/J63s7rHdxKua0i4oaIeLeo3F0RsX3HtkySJEmSJEmS5m8dDVo/BxwKPBMR65XLEBELRMQvgAeAIcDPO9JgRKwITAL2BZ4EzgVeBcYBj0fE4lXWszjweF7ulbyeJ/N6J0XEChXK/QK4F1gfuBk4G7gN+Aowqr3bJUmSJEmSJEnq+I0YNwROA44BHouInwE/TynNAYiI4cAfgDWBl4Dvp5T+1sE2LwGWBI5IKV1YWBkR5wBHAacDh1RRz8+BVYBzUkrHFNVzBHB+3s43igtExIHAj4ArgYNSSv8tSV+gPRskSZIkSZIkScp0aKR1SumLlNKxwGjgHeAU4JGIWDUifgI8AaxBFgAe3tGAdT7KehtgGnBxSfLJwAxg74jo10o9CwN75/nHlyRfBLwObFs82joiFiILiL9BmYA1ZPujDZsjSZIkSZIkSSrR0elBAEgpPQR8Dbga2Bh4HjgVeB/4RkrpBymlWTVoasv88e7CaO6iPkwHHgX65n1oycZAH+DRvFxxPXOAu0raA9iabAqQ64E5EfHNiDg2IsZFxCbt2hpJkiRJkiRJUhORUqpdZRH7ko2qXghIwIkppTNqWP8vgR8CP0wpnV0m/SLgMODQlNKvW6jnMLIR1RellA4vk/5D4JfAL/KR5ETEKcBPgTOBHcimPCn2ELBbSun9KrZjUoWkYSuvvHLf3/3ud61VMd+ZPj37bqF///5d3BNJtdStzu0PJ9e2voHr1rS6yVV0b92h8/42QPfYju6wDYMHT6fPgrPoP+fN2jXsc9GM50UH1Hgb5hfd6rVbUhOe31L31JXn9kEHHcRLL700OaVU9l6ILanJSOuIWDwirgMuA2aRTRPyb+C0iLgtIgbVoh1g0fzxkwrphfUDOqGeJfPHH5EF5DcH+gNrAXcDWwB/aaVdSZIkSZIkSVILOnojRiJiO+D3wCDgXmDflNJbEXFJvn4H4H8j4pCU0vUdba8LFQL8XwI7pZSm5f//X0TsArwIjIyITVJKj7dUUaVvFyJiUv/+/dcdNWpUjbrcfUycOBEA943UvXSrc/uaLVvP0xajavdLKIAtq+heunre3wboHtvRHbbh7LMnsu7Qlxj12TGtZ66Wz0UznhcdUONtmF90q9duSU14fkvdU1ee2x0Z3d2hkdYR8WvgVrIRyUemlLZJKb0FkFJ6P6W0E3AI2fzRf4mICRHRkbHohRHQi1ZIL6z/uBPqKfz9TFHAGoCU0kwa58HesJW2JUnzkIjqFkmSJEmSVBsdnR7kYGAysG5K6YJyGVJKvwOGA38Dvg8814H2XswfV6mQvnL+OLUT6imU+bhCmY/yxz6ttC1JkiRJkiRJqqCjQevTgE1SSi+0lCml9AqwGXAysEwH2nsgf9wmIpr0PR/BPQKYCTzRSj1PkM29PaJ05Hde7zYl7QHcRzaX9eqlbecKN2Z8rbWNkCRJkiRJkiSV16GgdUrppymlL6vMOyel9DNgkw609wrZTQ+HAoeVJJ8C9AOuSinNKKyMiGERMayknk+Bq/L840vq+UFe/10ppVeLyrwO3AIsB4wrLhAR2wDbko3CvrM92yZJkiRJkiRJqsGNGNsqpTS5g1UcCjwGXBARWwFTgI2ALcmm8/hJSf4p+WPpjKMnAKOAoyNiOPAksBowBniP5kFx8nXrAOdExDeBZ4DlgZ2B2cABKaVPypSTJEmSJEmSJFWh3SOtI6LDcze3p458tPX6wASyYPUxwIrA+cDGKaUPqqznA7JR3xcAK+X1bARcAayXt1Na5k1gPeAisnmvx5EFvm8BRqSUrmvr9kiSJEmSJEmSGnVkpPVrEXEG8JuU0udtKRgRawOnAk8DP2trwymlfwL7Vpm3dIR1cdqHZIHncZXylCnzPnB4vkiSJEmSJEmSaqgjc1rfBZwDvBMRv46ILVsaOR0RK0TE/4uIx4HJwNo0vdGhJEmSJEmSJGk+1+6R1imlfSLiIuB04KB8mR0RU4B3gI+A3sDiwKrAEmTzSr9HNu/0uW0doS1JkiRJkiRJ6t46dCPGlNJTwDYRsTKwP7AVMBz4WknW94HrgeuA61JKX3SkXUmSJEmSJElS99ShoHVBSukl4DiAiOgLLEM2wnoW8F5K6Z1atCNJkiRJkiRJ6t5qErQullKaCbyUL5IkSZIkSZIkVa0mQeuIWA7YAEjAUymlf9aiXkmSJEmSJEnS/KXDQeuI+BVwJNlNFgFSRJybUvpRR+uWJEmSJEmSJM1fenSkcER8BziaLGD9AvBi/vfReZokSZIkSZIkSVXrUNAaOAD4Evh6SmmNlNLqwLbAHGD/jnZOkiRJkiRJkjR/6WjQei3gppTSA4UVKaV7gZuA4R2sW5IkSZIkSZI0n+lo0HoxsmlBSr0ADOhg3ZIkSZIkSZKk+UxHg9Y9gC/KrP+CxhszSpIkSZIkSZJUlY4GrQFSDeqQJEmSJEmSJIleNahjfESML5cQEbPLrE4ppVq0K0mSJEmSJEnqZmoRPG7rNCBOGyJJkiRJkiRJKqtDQeuUUi2mF5EkSZIkSZIkCajNnNaSJEmSJEmSJNWEQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt0waC1JkiRJkiRJqhsGrSVJkiRJkiRJdcOgtSRJkiRJkiSpbhi0liRJkiRJkiTVDYPWkiRJkiRJkqS6YdBakiRJkiRJklQ3DFpLkiRJkiRJkuqGQWtJkiRJkiRJUt3o1dUdkCRJkqT5xjVR2/r2SrWtT5IkqQ440lqSJEmSJEmSVDcMWkuSJEmSJEmS6oZBa0mSJEmSJElS3TBoLUmSJEmSJP3/9u4/2PKyvg/4+4MkirhFoSU/Bs1GAuIkbQxmFKVNdmWKpE4jSWOnZaSpjaWJGPwBM2a0KqRNmsRBUTEaa9WUyNiZpNZmYgIzAmpA69RtmnECipLVOGqsEAki0uh++sf5Xnu93Lt77+7dPc859/WaOfPlfn98vs+zh2e+u+/z3OcAwxBaAwAAHKGqzb0AADg0oTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMNYyNC6qk6rqrdX1eer6sGq2l9V11TVY7ZY5+Tpuv1Tnc9PdU/b5PXPraqeXs8/vN4AAAAAALDi+Hk3YKuq6vQktyU5Ncl7k9yR5ClJXpTkgqo6t7vv3kSdU6Y6Zya5Kcm7k5yV5HlJnlVVT+vuuw5y/WOTXJvkq0kedUSdAgAAAAAgyWLOtP7NzALry7r7wu7+pe5+RpLXJXlCkl/ZZJ1fzSywfm13nzfVuTCz8PvU6T7rqqpK8o4kdyd5y2H3BAAAAACAb7NQofU0y/r8JPuTvGnN4VcnuT/JxVV14iHqPCrJxdP5V645fG2SzyR5ZlU9foMSlyV5Rmazsu/ffA8AAAAAADiYhQqtk+ydtjd294HVB7r7viS3JnlkknMOUeecJCckuXW6bnWdA0luWHO/b6mqJyb5tSSv7+4PbrkHAAAAAABsqLp73m3YtKp6TZIrklzR3Vevc/zaJJcmeUF3v/kgdS7NbEb1td39i+scvyLJa5L8Rne/bNX+45N8JMmuJE/q7geq6srMZnn/6+5+2yb78bENDp11xhlnPPKtb33rZsrsKPfdN/tsYdeuXXNuCbCdFmFs79u3ufPO3r3JEzfr5LO3tdxm+rEMfUiWox/L0IfTTrsvJ3znA9l14HPbd2PvxUMYF0fAe3FYFuHZDRwe4xuW0zzH9iWXXJI777xzX3c/eavXLtoXMZ40be/d4PjK/kcfpTqvSvIjSf5+dz9wiHsAAAAAALBFixZaz01VPTXJy5Nc3d0fPpJaG326UFUf27Vr19l79uw5kvJL6ZZbbkmS+LOB5bIIY3vvQxaKWl+/a5Mnbtae7f1NqM30Yxn6kCxHP5ahD1dffUvO3n1n9nz98u27sffiIYyLI+C9OCyL8OwGDo/xDctpnmP7SGZ3L9qa1iszoE/a4PjK/q9sZ51pWZD/nOSTSV55qEYCAAAAAHB4Fi20/sS0PXOD42dM209uc51HTec+McnXq6pXXpmtZ50k/3Had80h7g0AAAAAwAYWbXmQm6ft+VV1XHcfWDlQVbuSnJvka5l9WeLBfCTJA0nOrapd3X3fqjrHJTl/zf0eTPKfNqh1dmbrXP9xZmH4ES0dAgAAAACwky1UaN3dn66qGzMLlS9N8sZVh69KcmKS3+ru+1d2VtVZ07V3rKrz1aq6LsklSa5MsnqxxRcm2Z3khu6+azr/gSTPX69NVXVlZqH1b3f3246shwAAAAAAO9tChdaTFyS5Lckbquq8JLcneWqSvZkt5/GKNeffPm1rzf6XJ9mT5KVV9aQkH81s+Y9nJ/lSZqE4AAAAAADH0KKtaZ3u/nSSH03yzszC6suTnJ7k9UnO6e67N1nn7iRPS/KGJD8w1XlqknckefJ0HwAAAAAAjqFFnGmd7v6LJM/b5LlrZ1ivPnZPkhdNr8Nty5WZLTECAAAAAMARWriZ1gAAAAAALC+hNQAAAAAAwxBaAwAAAAAwjIVc0xqAJXLPvuT6vdtX76LevloAAADAMWemNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADCM4+fdAAAAABbIPfuS6/duX72LevtqAQBLwUxrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAbgqKk6+Gvfvnm3EAAAABiN0BoAAAAAgGEIrQEAAAAAGIbQGgAAAACAYQitAQAAAAAYhtAaAAAAAIBhCK0BAAAAABiG0BoAAIBUHfq1b9+8WwkA7ARCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIZx/LwbAAAAAMfc9bW99S7q7a0HADuYmdYAAAAAAAxDaA0AAAAAwDCE1gAAAAAADGMhQ+uqOq2q3l5Vn6+qB6tqf1VdU1WP2WKdk6fr9k91Pj/VPW2dc0+pqudX1Xuq6lNV9UBV3VtVf1xVP1dVC/lnCQAAAAAwkoX7IsaqOj3JbUlOTfLeJHckeUqSFyW5oKrO7e67N1HnlKnOmUluSvLuJGcleV6SZ1XV07r7rlWXPCfJm5N8IcnNST6b5LuS/HSStyX5iap6Tnf79g0AAAAAgMO0cKF1kt/MLLC+rLvfuLKzql6b5CVJfiXJz2+izq9mFli/trsvX1XnsiSvn+5zwarzP5nkJ5P8QXcfWHX+y5N8NMk/ySzA/r3D6xYAAAAAAAu1pMU0y/r8JPuTvGnN4VcnuT/JxVV14iHqPCrJxdP5V645fG2SzyR5ZlU9fmVnd9/U3b+/OrCe9n8xyVumH/dsoTsAAAAAAKyxUKF1kr3T9sZ1wuP7ktya5JFJzjlEnXOSnJDk1um61XUOJLlhzf0O5W+m7Tc2eT4AAAAAAOuoRVqCuapek+SKJFd099XrHL82yaVJXtDdbz5InUszm1F9bXf/4jrHr0jymiS/0d0vO0Sbjk/yv5L8UJILuvuGg50/XfOxDQ6ddcYZZzzyrW9966FK7Dj33Tf7bGHXrl1zbgmwFfv2Hfz4aafdlxO+84HsOvC57bvpyWdvX60cug8rzt69yRM3aw79WIY+JMvRj2Xow7KM72V4L5Ll6Mcy9CEZux/LMrY37Z5x3wuYB//uhuU0z7F9ySWX5M4779zX3U/e6rWLNtP6pGl77wbHV/Y/+hjVSZJfyyywft9mAmsAAAAAADa2iF/EOIzpSxsvT3JHZmtkb8pGny5U1cd27dp19p49e7angUvklltuSZL4s4HFsvcQiyxdffUtOXv3ndnz9csPfuJW7Nne3yA6VB9W9Ls2u6LUJs2hH8vQh2Q5+rEMfViW8b0M70WyHP1Yhj4kY/djWcb2pl0/7nsB8+Df3bCc5jm2j2R296LNtF6ZAX3SBsdX9n/laNepqhcmeX2SP0uyt7vvOcQ9AQAAAAA4hEULrT8xbc/c4PgZ0/aTR7NOVb04yRuTfDyzwPqLh7gfAAAAAACbsGih9c3T9vyq+ra2V9WuJOcm+VqSjxyizkeSPJDk3Om61XWOS3L+mvutPv6yJK9L8ieZBdZf2mIfAAAAOEqqNvcCAMa1UKF1d386yY1Jdie5dM3hq5KcmOS67r5/ZWdVnVVVZ62p89Uk103nX7mmzgun+jd0912rD1TVKzP74sWPJTmvu798ZD0CAAAAAGC1RfwixhckuS3JG6rqvCS3J3lqkr2ZLefxijXn3z5t136W/vIke5K8tKqelOSjSZ6Y5NlJvpQ1oXhV/WySX07yzSQfSnJZPfTj+f3d/c7D6xbAYbh+m6cJXeQLhAAAAID5WrjQurs/XVU/mlmAfEGSf5TkC5l9KeJV3f1Xm6xzd1U9Lcmrk1yY5B8kuTvJO5K8qrs/t+aS75+2D0vy4g3KfiDJOzfbFwAAAAAAvt3ChdZJ0t1/keR5mzx3w2mI3X1PkhdNr0PVuTIPXUoEAAAAAIBttFBrWgMAAAAAsNyE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAwhNYAAAAAAAxDaA0AAAAAwDCE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAwhNYAAAAAAAxDaA0AAAAAwDCE1gADqtrcCwAAAGDZCK0BAAAAABiG0BoAAAAAgGEIrQEAAAAAGIbQGgAAAACAYQitAQAAAAAYhtAaAAAAAIBhCK0BAAAAABiG0BoAAAAAgGEIrQEAAAAAGIbQGgAAAACAYQitAQAAAAAYhtAaAAAAAIBhCK0BAAAAABiG0BoAAAAAgGEIrQEAAAAAGIbQGgAAAACAYRw/7wYAAAAAh+H62t56F/X21gOAw2SmNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAMBAqjb3AoBlJbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhnH8vBsAMDfX1/bVuqi3rxYAAADADmamNQAAAAAAwxBaAwAAAAAwDMuDAAAAAPOzncv2JZbuA1gCZloDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1sHSqNvcCAAAAYDxCawAAAAAAhiG0BgAAAABgGEJrAAAAYNtZtg+AwyW0BgAAAABgGEJrAAAAAACGIbQGAAAAAGAYQmsAAAAAAIYhtAYAAAAAYBhCawAAAAAAhiG0BgAAAABgGEJrAAAAAACGcfy8GwAAAACw0K6v7a13UW9vPYAFY6Y1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAKyjanMvALaX0BoAAAAAgGEcP+8GAAvo+m2eSnBRb289AAAAABaWmdYAAAAAAAzDTGsAAAAAknv2Jdfv3b56fqsWOExmWgMAAAAAMAyhNfAtvhkbAAAAgHkTWgMAAAAAMAyhNQAAAMAS28xv1O7bN+9WAvx/CxlaV9VpVfX2qvp8VT1YVfur6pqqeswW65w8Xbd/qvP5qe5pR/veAAAAAAA81PHzbsBWVdXpSW5LcmqS9ya5I8lTkrwoyQVVdW53372JOqdMdc5MclOSdyc5K8nzkjyrqp7W3XcdjXsDAAAAcBRcv81fxHRRb289YFMWcab1b2YWGl/W3Rd29y919zOSvC7JE5L8yibr/GpmgfVru/u8qc6FmQXQp073OVr3BgAAAABgHQs103qa6Xx+kv1J3rTm8KuTXJLk4qq6vLvvP0idRyW5OMn9Sa5cc/jaJC9N8syqevzKbOvtujds66e+PvEFAABgB6hN/lO633V023HMmDHODrdoM633Ttsbu/vA6gPdfV+SW5M8Msk5h6hzTpITktw6Xbe6zoEkN6y533bemyW1mS+22OxDFgAAAAB2qupenE9aquo1Sa5IckV3X73O8WuTXJrkBd395oPUuTSzGdXXdvcvrnP8iiSvSfIb3f2y7bz3dO7HNjj0ww9/+MMf9rjHPe5gly+dBx449Dnf8R0HclwdyHH5m+278cNO2L5a2Vw/kuSE79zkiZuxDH1IlqMfy9CH5Jj3w9g+iDn0Yxn6kCxHP5ahD8syvpfhvUiWox/L0Idk7H7spLGdLP57kYzdh2Q5+rEMfUiWY3zvpPciGbsfy9CHZHn6cSgHDszm3h533LGfu/zZz342Dz744D3dfcpWr12o5UGSnDRt793g+Mr+Rx+FOtt174P55oMPPnjvnXfeuf8Iaiyrs6btHXNtBbDdjG1YXsY3LCdjG5aX8Q3LaZ5je3eSvz6cCxcttF4K3f3kebdh0azMTvdnB8vF2IblZXzDcjK2YXkZ37CcFnVsL9qa1iuzmU/a4PjK/q8chTrbdW8AAAAAADawaKH1J6btmRscP2PafvIo1NmuewMAAAAAsIFFC61vnrbnV9W3tb2qdiU5N8nXknzkEHU+kuSBJOdO162uc1yS89fcbzvvDQAAAADABhYqtO7uTye5MbNFvC9dc/iqJCcmua6771/ZWVVnVdVZq0/s7q8muW46/8o1dV441b+hu+86knsDAAAAALA1i/hFjC9IcluSN1TVeUluT/LUJHszW5rjFWvOv33a1pr9L0+yJ8lLq+pJST6a5IlJnp3kS3loMH049wYAAAAAYAuqu+fdhi2rqscm+eUkFyQ5JckXkrwnyVXd/Vdrzu0k6e61oXWq6uQkr05yYZLvSXJ3kj9M8qru/tyR3hsAAAAAgK1ZyNAaAAAAAIDltFBrWgMAAAAAsNyE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAwhNYAAAAAAAxDaM3Qquq0qnp7VX2+qh6sqv1VdU1VPWbebQMO3zSWe4PXF+fdPmBjVfUzVfXGqvpQVf31NG5/5xDXPL2q3ldV91TVA1X1p1X14qp62LFqN3BoWxnfVbX7IM/yrqp3H+v2A+urqlOq6vlV9Z6q+tT0LL63qv64qn6uqtbNhjy/YWxbHduL9uw+ft4NgI1U1elJbktyapL3JrkjyVOSvCjJBVV1bnffPccmAkfm3iTXrLP/q8e4HcDW/NskP5zZWP1ckrMOdnJVPTvJ7yX5epL/kuSeJP84yeuSnJvkOUezscCWbGl8T/53kv+2zv6Pb1+zgCP0nCRvTvKFJDcn+WyS70ry00neluQnquo53d0rF3h+w0LY8tieLMSzux7abhhDVd2Q5Pwkl3X3G1ftf22SlyT5re7++Xm1Dzh8VbU/Sbp793xbAmxVVe3NLMz6VJIfz+wvyO/q7ueuc+7fms47Kcm53f0/p/2PSHJTkqcl+efdPdSsDtiptji+dyf58yS/3d3/8hg2E9iiqnpGkhOT/EF3H1i1/7uTfDTJY5P8THf/3rTf8xsWwGGM7d1ZoGe35UEY0jTL+vwk+5O8ac3hVye5P8nFVXXiMW4aAOxo3X1zd9+5zoyN9fxMkr+T5N0r/+Cdanw9sxmdSfILR6GZwGHY4vgGFkR339Tdv7861Jr2fzHJW6Yf96w65PkNC+AwxvZCsTwIo9o7bW9cZ/DdV1W3ZhZqn5Pk/ce6ccC2eHhVPTfJ4zL7IOpPk3ywu78532YB2+gZ0/aP1jn2wSRfS/L0qnp4dz947JoFbKPvrap/k+SUJHcn+XB3/+mc2wRs3t9M22+s2uf5DYtvvbG9YiGe3UJrRvWEafvJDY7fmVlofWaE1rCovjvJdWv2/XlVPa+7PzCPBgHbbsPneXd/o6r+PMkPJnl8ktuPZcOAbfMPp9e3VNUtSX62uz87lxYBm1JVxyf5F9OPqwNqz29YYAcZ2ysW4tlteRBGddK0vXeD4yv7H330mwIcBe9Icl5mwfWJSf5ukt9KsjvJH1bVD8+vacA28jyH5fW1JP8uyZOTPGZ6rayDvSfJ+y3lB8P7tSQ/lOR93X3Dqv2e37DYNhrbC/XsFloDcMx191XT+lt/2d1f6+6PT1+s+tokJyS5cr4tBAAOpru/1N2v6u593f2V6fXBzH4b8n8k+YEkz59vK4GNVNVlSS5PckeSi+fcHGCbHGxsL9qzW2jNqFY+uT1pg+Mr+79y9JsCHEMrXxbxY3NtBbBdPM9hh+nubyR52/Sj5zkMqKpemOT1Sf4syd7uvmfNKZ7fsIA2MbbXNeqzW2jNqD4xbc/c4PgZ03ajNa+BxfR/pu0wv5IEHJENn+fTWnvfn9mXw9x1LBsFHHWe5zCoqnpxkjcm+XhmodYX1znN8xsWzCbH9sEM9+wWWjOqm6ft+VX1bf+fVtWuJOdmthbPR451w4Cj6pxp6y/AsBxumrYXrHPsx5I8Mslt3f3gsWsScAx4nsOAquplSV6X5E8yC7W+tMGpnt+wQLYwtg9muGe30Johdfenk9yY2ZeyXbrm8FWZffJzXXfff4ybBhyhqnriel/uUFW7k1w7/fg7x7RRwNHyu0m+nOSfVdWPruysqkck+ffTj2+eR8OAI1NVZ6+dXDLtPy/JS6YfPc9hEFX1ysy+nO1jSc7r7i8f5HTPb1gQWxnbi/bsru6edxtgXVV1epLbkpya5L1Jbk/y1CR7M1sW5Ondfff8Wggcjqq6MrMvhvhgks8kuS/J6UmeleQRSd6X5Ke6+//Oq43AxqrqwiQXTj9+d5JnZjYj40PTvi939xVrzv/dJF9P8u4k9yT5ySRPmPb/0/YXUhjCVsZ3Vd2S2ZJ9tyX53HT87yV5xvTfr+zulXALmKOq+tkk70zyzcyWD7h3ndP2d/c7V11zYTy/YWhbHduL9uwWWjO0qnpskl/O7NeSTknyhSTvSXJVd//VPNsGHJ6q+vEkP5/kRzL7B/GJmX2Jy58kuS6z36LwcIJBTR88vfogp3ymu3evuebcJK9I8rTMPpz6VJK3J3lDd3/z6LQU2KqtjO+q+rkkP5Xkh5L87STfkeQvk3w4ybXd/aGNigDH1ibGdpJ8oLv3rLnO8xsGttWxvWjPbqE1AAAAAADDsKY1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwAAAAAwDKE1AAAAAADDEFoDAAAAADAMoTUAAAAAAMMQWgMAAAAAMAyhNQAAAAAAwxBaAwDADlBVu6uqq+qd824LAAAcjNAaAAAAAIBhCK0BAAAAABiG0BoAAAAAgGEIrQEAYAerquOq6vXTetf/tapOmHebAADY2Y6fdwMAAID5qKpHJHlXkp9O8qYkl3X3gfm2CgCAnU5oDQAAO1BVnZzkvyd5epJf6u5fn3OTAAAgidAaAAB2nKr6viR/lOT0JBd397vm3CQAAPgWoTUAAOwsT0jy4SQnJvmJ7n7/nNsDAADfxhcxAgDAznJmku9JcleSfXNuCwAAPITQGgAAdpbfT/LyJE9K8v6qOmW+zQEAgG8ntAYAgB2mu/9Dkpck+ZEkt1TVd825SQAA8C1CawAA2IG6+5okv5DkB5N8oKq+d74tAgCAGaE1AADsUN39liT/KskZST5YVY+bc5MAAEBoDQAAO1l3vzPJc5N8X2bB9ePn2yIAAHa66u55twEAAAAAAJKYaQ0AAAAAwECE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAwhNYAAAAAAAxDaA0AAAAAwDCE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAwhNYAAAAAAAxDaA0AAAAAwDCE1gAAAAAADENoDQAAAADAMITWAAAAAAAMQ2gNAAAAAMAw/h/JasbI4GsFVQAAAABJRU5ErkJggg==",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 43,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 440,
|
|
"width": 726
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# definiujemy zmienną losową X o dwumianowym rozkładzie prawdopodobieństwa z parametrami n=100 i p=0.1\n",
|
|
"X = stats.binom(100, 0.1)\n",
|
|
"x_binom = np.arange(0, 25) # wartości dla rozkładu dwumianowego\n",
|
|
"pmf_binom = X.pmf(x_binom)\n",
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|
"\n",
|
|
"# definiujemy zmienną losową Y o rozkładzie Poissona z parametrem lambda=10\n",
|
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"Y = stats.poisson(10)\n",
|
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"x_poisson = np.arange(0, 25) # wartości dla rozkładu Poissona\n",
|
|
"pmf_poisson = Y.pmf(x_poisson)\n",
|
|
"\n",
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"# tworzenie wykresu dla obu rozkładów\n",
|
|
"plt.bar(x_binom, pmf_binom, width=0.4, label='Binomial PMF (n=100, p=0.1)', color='blue', align='center')\n",
|
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"plt.bar(x_poisson, pmf_poisson, width=0.4, label='Poisson PMF (lambda=10)', color='orange', align='edge')\n",
|
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"\n",
|
|
"plt.title('Funkcje masy prawdopodobieństwa - rozkład dwumianowy i Poissona')\n",
|
|
"plt.xlabel('k')\n",
|
|
"plt.ylabel('P(X=k), P(Y=k)')\n",
|
|
"plt.legend()\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c51ae2",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"### Rozkład normalny\n",
|
|
"\n",
|
|
"**Rozkład normalny** $\\mathcal{N}(\\mu, \\sigma)$ jest przykładem rozkładu ciągłego i zadany jest przez **gęstość**\n",
|
|
"$$f_{\\mu,\\sigma}(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}\\exp\\left(\\frac{-(x-\\mu)^2}{2\\sigma^2} \\right), $$\n",
|
|
"gdzie parametry $\\mu$ i $\\sigma$ oznaczają odpowiednio wartość oczekiwaną i odchylenie standardowe. Specjalnym przypadkiem jest **standardowy rozkład normalny** $\\mathcal{N}(0, 1)$, czyli rozkład normalny o parametrach $\\mu=0$ i $\\sigma=1$, dla którego gęstość dana jest wzorem\n",
|
|
"$$f(x) = f_{1, 0}(x) = \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(\\frac{-x^2} 2\\right).$$ \n",
|
|
"W przypadku rozkładów ciągłych prawdopodobieństwo wyznacza się poprzez obliczenie odpowiedniej całki oznaczonej. Np. jeśli $X\\sim\\mathcal{N}(0,1)$, to dla dowolnego zbioru (borelowskiego) $A$ zachodzi\n",
|
|
"$$\\mathbb{P}(X\\in A) = \\int_{A} f(x)dx = \\int_{A} \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(\\frac{-x^2} 2\\right) dx,$$\n",
|
|
"co możemy interpretować w ten sposób, że pole pod wykresem gęstości na zbiorze $A$ jest szukanym prawdopodobieństwem, a tym samym \n",
|
|
"$$\\mathbb{P}(X\\in \\mathbb{R}) = \\int_{-\\infty}^{\\infty} f(x)dx = 1.$$\n",
|
|
"Obliczanie takich całek w wielu sytuacjach jest bardzo skomplikowane (rozkład normalny jest tutaj dobrym przykładem) i wymaga zastosowania odpowiednich metod numerycznych.\n",
|
|
"\n",
|
|
"Rozkład normalny jest jednym z najważniejszych rozkładów prawdopodobieństwa i ma ogromne zastosowanie przede wszystkim w statystyce. Zobaczmy na początek jak wygląda gęstość standardowego rozkładu normalnego. Ponieważ rozkład normalny z dowolnymi parametrami da się uzyskać ze standardowego rozkładu normalnego przez odpowiednie przeskalowanie, wykres ten będzie miał zawsze taki sam kształt a reprezentująca go krzywa zwana jest **krzywą Gaussa** lub **krzywą dzwonową** (ze względu na swój kształt)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 45,
|
|
"id": "cec2f6",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
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",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 45,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 441,
|
|
"width": 726
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# argumenty x gęstości standardowego rozkładu normalnego\n",
|
|
"x = np.linspace(-4, 4, 1000)\n",
|
|
"pdf_values = stats.norm.pdf(x)\n",
|
|
"\n",
|
|
"# tworzenie wykresu\n",
|
|
"plt.plot(x, pdf_values, label='gęstość f(x) standardowego rozkładu normalnego', color='green')\n",
|
|
"plt.title('Funkcja gęstości prawdopodobieństwa dla rozkładu normalnego standardowego')\n",
|
|
"plt.xlabel('x')\n",
|
|
"plt.ylabel('f(x)')\n",
|
|
"plt.grid()\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0436fe",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"**Przykład 6**\n",
|
|
"\n",
|
|
"Tym razem porównamy rozkład normalny z rozkładem Poissona. Ponieważ rozkład normalny jest rozkładem ciągłym, a rozkład Poissona jest rozkładem dyskretnym, porównamy dystrybuanty obu rozkładów na przykładzie zmiennych losowych $Z \\sim \\mathcal{N}(\\mu, \\sigma)$ i $Y \\sim Po(\\lambda)$. Parametry dobierzemy w taki sposób, aby\n",
|
|
"$$\\mathbb{E}(Z) = \\mu = \\lambda = \\mathbb{E}(Y) \\quad \\text{oraz} \\quad Var(Z) = \\sigma^2 = \\lambda = Var(Y).$$\n",
|
|
"Okazuje się, że jeśli tylko $\\lambda$ jest duża i zachodzą powyższe równości, to rozkład Poissona dobrze przybliża rozkład normalny. Zatem przyjmijmy, że $Z \\sim \\mathcal{N}(100, 10)$ i $Y \\sim Po(100)$, a następnie narysujmy wykresy obydwu dystrybuant."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 48,
|
|
"id": "197497",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 48,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 440,
|
|
"width": 720
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# definiujemy parametry dla rozkładu normalnego\n",
|
|
"mu = 100\n",
|
|
"sigma = 10\n",
|
|
"x_norm = np.linspace(mu - 4*sigma, mu + 4*sigma, 1000)\n",
|
|
"cdf_norm = stats.norm.cdf(x_norm, mu, sigma)\n",
|
|
"\n",
|
|
"# definiujemy parametry dla rozkładu Poissona\n",
|
|
"lambda_poisson = 100\n",
|
|
"x_poisson = np.arange(0, 150) # Adjusted range for visualization\n",
|
|
"cdf_poisson = stats.poisson.cdf(x_poisson, lambda_poisson)\n",
|
|
"\n",
|
|
"# tworzenie wykresu\n",
|
|
"plt.plot(x_norm, cdf_norm, label='dystrybuanta rozkładu normalnego (mu=100, sigma=10)', color='green')\n",
|
|
"plt.step(x_poisson, cdf_poisson, label='dystrybuanta rozkładu Poissona (lambda=100)', color='orange', where='post')\n",
|
|
"\n",
|
|
"plt.title('Dystrybuanty rozkładu normalnego i rozkładu Poissona')\n",
|
|
"plt.xlabel('x')\n",
|
|
"plt.ylabel('F(x)')\n",
|
|
"plt.legend()\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f3b5ba",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"## Bibliografia\n",
|
|
"\n",
|
|
"Dokumentację dotyczącą omawianych pakietów można znaleźć na stronach:\n",
|
|
"* [NumPy](https://numpy.org/doc/stable/#)\n",
|
|
"* [SciPy](https://docs.scipy.org/doc/scipy/index.html)\n",
|
|
"* [Matplotlib](https://matplotlib.org/stable/users/index)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"id": "330537",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "raw",
|
|
"id": "b764e2",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"argv": [
|
|
"/usr/bin/python3",
|
|
"-m",
|
|
"ipykernel",
|
|
"--HistoryManager.enabled=False",
|
|
"--matplotlib=inline",
|
|
"-c",
|
|
"%config InlineBackend.figure_formats = set(['retina'])\nimport matplotlib; matplotlib.rcParams['figure.figsize'] = (12, 7)",
|
|
"-f",
|
|
"{connection_file}"
|
|
],
|
|
"display_name": "Python 3 (system-wide)",
|
|
"env": {
|
|
},
|
|
"language": "python",
|
|
"metadata": {
|
|
"cocalc": {
|
|
"description": "Python 3 programming language",
|
|
"priority": 100,
|
|
"url": "https://www.python.org/"
|
|
}
|
|
},
|
|
"name": "python3",
|
|
"resource_dir": "/ext/jupyter/kernels/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": "3.10.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
} |