{ "cells": [ { "cell_type": "markdown", "id": "8683b2", "metadata": { "collapsed": false }, "source": [ "# Zmienne losowe i ich rozkłady. Funkcja masy prawdopodobieństwa. Dystrybuanta. Wartość oczekiwana.\n" ] }, { "cell_type": "markdown", "id": "f97929", "metadata": { "collapsed": false }, "source": [ "**Treści kształcenia:** Jednowymiarowe zmienne losowe. Dystrybuanta i jej własności. Przegląd podstawowych rozkładów dyskretnych (dwumianowy, Poissona, geometryczny, Pascala, hipergeometryczny). \n", "\n", "**Efekty kształcenia:** Student/ka potrafi wyznaczyć rozkład prawdopodobieństwa zmiennej losowej; potrafi obliczyć wartość oczekiwaną, wariancję, współczynnik korelacji zmiennych losowych; potrafi określić, czy podane zmienne losowe są niezależne." ] }, { "cell_type": "markdown", "id": "846b5b", "metadata": { "collapsed": false }, "source": [ "## Wstęp\n", "\n", "Do tej pory rozważając różnorodne doświadczenia losowe, zaczynaliśmy od zdefiniowania przestrzeni probabilistycznej i interesujących nas zdarzeń. Zauważmy jednak, że często przy definicji zdarzeń używaliśmy różnych liczb powiązanych z danym eksperymentem np. sumy oczek w $n$ rzutach kostką, liczby sukcesów w $n$ próbach Bernoulliego, czasu przyjścia osoby na spotaknie, gdy wiemy, że ten czas jest losowy itp. W takich sytuacjach przy modelowaniu danego eksperymentu możemy posłużyć się pewnymi wartościami liczbowymi związanymi z wynikiem naszego eksperyementu losowego, które będziemy nazywać **zmiennymi losowymi** i które stanowią główny temat tych i kilku kolejnych zajęć." ] }, { "cell_type": "markdown", "id": "06531a", "metadata": { "collapsed": false }, "source": [ "## Definicja zmiennych losowych\n", "\n", "Zmienna losowa to po prostu funkcja, która zwraca informacje o pewnych wartościach liczbowych związanych z danym eksperymentem losowym, zależnych od wyniku tego eksperymentu. Poniżej przedstawimy formalną definicję tego pojęcia.\n", "\n", "**Definicja (zmienna losowa):**\n", " \n", "**Zmienną losową** nazywamy funkcję (mierzalną) $X:\\Omega\\to\\mathbb R$ działającą z przestrzeni probabilistycznej $(\\Omega, \\mathcal{F}, \\mathbb{P})$ do zbioru liczb rzeczywistych $\\mathbb R$.\n", "\n", "Zmienne losowe najczęściej będziemy oznaczać dużymi literami z końca alfabetu ($X$, $Y$, $Z$ itp.).\n", "\n", "**Przykład 1**\n", "\n", "Rozważmy eksperyment polegający na dwukrotnym rzucie czworościenną kostką do gry. W tym przypadku jako zbiór zdarzeń elementarnych $\\Omega$ możemy przyjąć wszystkie pary liczb $(x,y)$, gdzie $x,y\\in\\{1,2,3,4\\}$. Oczywiście mamy tutaj do czynienia z modelem klasycznym. Zdefiniujmy następujące zmienne losowe:\n", "\n", "* zmienna losowa $X$ zwracająca sumę wyrzuconych oczek,\n", "* zmienna losowa $Y$ zwracająca liczbę wyrzuconych jedynek.\n", "\n", "Ponieważ zmienna losowa to funkcja przypisująca liczby rzeczywiste zdarzeniom elementarnym, to powyżej zdefiniowany zbiór $\\Omega$ stanowi dziedzinę zarówno funkcji $X$, jak i $Y$. Musimy jeszcze podać wzory tych funkcji.\n", "\n", "Zacznijmy od zmiennej losowej $X$ i przykładowego zdarzenia elementarnego $\\omega=(1,1)$. Ponieważ $X$ ma zwracać informację o sumie wyrzuconych oczek, to możemy przyjąć, że $X(\\omega) = X((1,1))=1+1=2.$ W analogiczny sposób możemy wyznaczyć wartości tej funkcji dla pozostałych zdarzeń elementarnych:\n", "\n", "* $X((1,2))=X((2,1))=3$,\n", "* $X((2,2))=X((1,3))=X((3,1))=4$,\n", "* $X((1,4))=X((4,1))=X((2,3))=X((3,2))=5$,\n", "* $X((3,3))=X((2,4))=X((4,2))=6$,\n", "* $X((4,3))=X((3,4))=7$,\n", "* $X((4,4))=8$.\n", "\n", "Zajmiemy się teraz zmienną losową $Y$. Ta zmienna losowa ma zwracać informację o liczbie wyrzuconych jedynek, więc przykładowo $Y((1,1))=2$. W analogiczny sposób możemy wyznaczyć pozostałe wartości tej funkcji:\n", "\n", "* $Y((1,2))=Y((1,3))=Y((1,4))=Y((2,1))=Y((3,1))=Y((4,1))=1$,\n", "* $Y((2,2))=Y((2,3))=Y((2,4))=Y((3,2))=Y((3,3))=Y((3,4))=Y((4,2))=Y((4,3))=Y((4,4))=0$.\n", "\n", "**Przykład 2**\n", "\n", "Arek i Bartek umówili się na spotkanie. Każdy z nich przychodzi na to spotkanie w losowym momencie między 17:00 a 17:30. W tym przypadku możemy przyjąć, że zbiór zdarzeń elementarnych to $\\Omega=\\{(a,b): a, b\\in [0,30]\\}$, gdzie $a$ i $b$ oznaczają odpowiednio czas przyjścia Arka i Bartka na spotkanie liczony w minutach po godzinie 17:00, z prawdopodobieństwem geometrycznym. Zdefiniujmy następujące zmienne losowe:\n", "\n", "* $T$ - czas przyjścia Arka,\n", "* $W$ - czas oczekiwania Bartka na przyjście Arka zaokrąglony w górę do pełnych minut. Zakładamy, że jeśli Arek przyjdzie przed Bartkiem, to za wartość zmiennej losowej $W$ przyjmujemy $0$.\n", "\n", "Dziedziną zmiennych losowych $T$ i $W$ jest zbiór $[0,30]\\times [0,30]$. Pozostaje nam podać wzory tych funkcji:\n", "\n", "* $\\forall_{(a,b)\\in\\Omega}\\,T((a,b))=a$,\n", "* $\\forall_{(a,b)\\in\\Omega}\\, W((a,b))=\\begin{cases} 0, & \\text{ jeśli } a \\leq b, \\\\ \\lceil a-b \\rceil, & \\text{ jeśli } a>b.\\end{cases}$\n", "\n", "Oznaczenie: $\\lceil x\\rceil$ oznacza najmniejszą liczbę całkowitą większą lub równą $x$, czyli tzw. sufit z liczby $x$.\n", "\n", "Dziedziną zmiennej losowej jest $\\Omega$, czyli zbiór wszystkich możliwych wyników pewnego doświadczenia losowego. Możemy zatem liczyć prawdopodobieństwo tego, że dana zmienna losowa osiągnie pewne wartości odwołując się do odpowiednich zdarzeń elementarnych. W tym celu wprowadźmy następujące oznaczenia. Dla $A\\subseteq \\mathbb{R}$ niech \n", "$$\\mathbb{P}(X\\in A)=\\mathbb{P}(X^{-1}(A))=\\mathbb{P}(\\{\\omega\\in\\Omega: X(\\omega)\\in A\\}).$$\n", "\n", "Jeśli $A$ będzie zbiorem jednopunktowym, tzn. $A=\\{a\\}$ dla pewnej liczby rzeczywistej $a$, to będziemy też pisać $\\mathbb{P}(X=a)$ zamiast $\\mathbb{P}(X\\in\\{a\\})$. Jeśli natomiast $A$ będzie przedziałem, np. $A=(a,b)$ dla pewnych $a,b\\in\\mathbb{R}$, to będziemy stosować zapis $\\mathbb{P}(a0$ dla każdego $a_i\\in A$ oraz \n", "\n", "$$\\mathbb{P}(X\\in A)=\\sum_{a_i\\in A}\\mathbb{P}(X=a_i)=1.$$\n", "\n", "**Przykład 4** \n", "\n", "Sprawdź, które ze zmiennych losowych zdefiniowanych w przykładach 1. i 2. są dyskretne.\n", "\n", "Zacznijmy od zmiennej losowej $X$, która zwraca informację o sumie oczek wyrzuconych w dwóch rzutach czworościenną kostką. Na podstawie przykładu 1. możemy stwierdzić, że zbiorem wartości funkcji $X$ jest zbiór $\\{2, 3, 4, 5, 6, 7, 8\\}$. Sprawdzimy, że elementy tego zbioru to faktycznie atomy:\n", "\n", "* $\\mathbb{P}(X=2)=\\mathbb{P}(\\{(1,1)\\})=\\frac{1}{16}>0$,\n", "* $\\mathbb{P}(X=3)=\\mathbb{P}(\\{(1,2), (2,1)\\})=\\frac{1}{8}>0$,\n", "* $\\mathbb{P}(X=4)=\\mathbb{P}(\\{(1,3), (3,1), (2,2)\\})=\\frac{3}{16}>0$,\n", "* $\\mathbb{P}(X=5)=\\mathbb{P}(\\{(1,4), (4,1), (2,3), (3,2)\\})=\\frac{1}{4}>0$,\n", "* $\\mathbb{P}(X=6)=\\mathbb{P}(\\{(2,4), (4,2), (3,3)\\})=\\frac{3}{16}>0$,\n", "* $\\mathbb{P}(X=7)=\\mathbb{P}(\\{(3,4), (4,3)\\})=\\frac18>0$,\n", "* $\\mathbb{P}(X=8)=\\mathbb{P}(\\{(4,4)\\})=\\frac{1}{16}>0$.\n", "\n", "Możemy też łatwo stwierdzić, że $\\mathbb{P}(X\\in \\{2,3,4,5,6,7,8\\})=\\mathbb{P}(\\Omega)=1$. Zatem zmienna losowa $X$ jest dyskretna, a jej zbiór atomów to $\\{2,3,4,5,6,7,8\\}$.\n", "\n", "W analogiczny sposób możemy sprawdzić, że zmienne losowe $Y$ z przykładu 1. i $W$ z przykładu 2. również są dyskretne, a ich zbiory atomów to odpowiednio $\\{0,1,2\\}$ i $\\{0,1,2,\\ldots, 30\\}$. \n", "\n", "Pozostaje nam jeszcze zmienna losowa $T$, która oznacza czas przyjścia Arka na spotkanie. Widzimy, że zbiór wartości tej funkcji to przedział $[0,30]$, który jest zbiorem nieprzeliczalnym. Ponadto pokazaliśmy w przykładzie 3., że $\\mathbb{P}(T=15)=0$. W analogiczny sposób można pokazać, że $\\mathbb{P}(T=a)=0$ dla dowolnej liczby rzeczywistej $a$. Zatem ta zmienna losowa w ogóle nie ma atomów i tym samym nie może być dyskretną zmienną losową." ] }, { "cell_type": "markdown", "id": "7a13be", "metadata": { "collapsed": false }, "source": [ "## Rozkład prawdopodobieństwa zmiennej losowej\n", "\n", "Z każdą zmienną losową związane jest pojęcie rozkładu prawdopodobieństwa, który jest po prostu pewną miarą (zwaną miarą probabilistyczną) określoną na zbiorze wartości zmiennej losowej. Intuicyjnie rzecz ujmując, miara ta mówi w jaki sposób prawdopodobieństwo ,,rozkłada się\" albo jest podzielone pomiędzy poszczególne wartości przyjmowane przez zmienną losową.\n", "\n", "**Definicja (rozkład prawdopodobieństwa zmiennej losowej)**\n", "\n", "**Rozkładem prawdopodobieństwa** zmiennej losowej $X$ nazywamy funkcję $\\mu_X$, która wszystkim zbiorom (borelowskim) $B\\subseteq \\mathbb{R}$ przypisuje wartość prawdopodobieństwa\n", "\n", "$$\\mu_X(B) = \\mathbb{P}(X^{-1}(B)). $$\n", "\n", "W celu podania rozkładu prawdopodobieństwa zmiennej losowej dyskretnej wystarczy podać wartości\n", "\n", "$$p_i=\\mathbb{P}(X=a_i)$$\n", "\n", "dla wszystkich atomów $a_i\\in A$. Jest to tzw. **funkcja masy prawdopodobieństwa** tej zmiennej losowej. Czasem nazywamy ją po prostu **rozkładem** zmiennej losowej dyskretnej.\n", "\n", "Jeśli mamy daną funkcję masy prawdopodobieństwa dyskretnej zmiennej losowej $X$, to prawdopodobieństwo, że przyjmie ona wartości z danego zbioru $B$ możemy określić sumując prawdopodobieństwa tych atomów tej zmiennej losowej, które należą do zbioru $B$, tzn.:\n", "\n", "$$\\mathbb{P}(X\\in B)=\\sum_{a_i\\in A \\cap B} \\mathbb{P}(X=a_i)=\\sum_{a_i\\in A\\cap B} p_i,$$\n", "\n", "gdzie $A$ jest zbiorem atomów zmiennej losowej $X$.\n", "\n", "**Przykład 5**\n", "\n", "Na podstawie obliczeń z przykładu 4. możemy podać funkcję masy prawdopodobieństwa zmiennej losowej $X$ zliczającej sumę oczek w dwóch rzutach czworościenną kostką:\n", "\n", "$$p_0=\\mathbb{P}(X=2)=\\frac{1}{16}, \\quad p_1=\\mathbb{P}(X=3)=\\frac{1}{8}, \\quad p_2=\\mathbb{P}(X=4)=\\frac{3}{16}, \\quad p_3=\\mathbb{P}(X=5)=\\frac{1}{4}, $$\n", "$$p_4=\\mathbb{P}(X=6)=\\frac{3}{16}, \\quad p_5=\\mathbb{P}(X=7)=\\frac{1}{8}, \\quad p_6=\\mathbb{P}(X=8)=\\frac{1}{16}.$$\n", "\n", "Funkcję masy prawdopodobieństwa możemy też zapisać, używając tabelki:\n", "\n", "| $k$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |\n", "| --- | --- | --- | --- | --- | --- | --- | --- |\n", "| $\\mathbb{P}(X=k)$ | $\\frac{1}{16}$ | $\\frac{1}{8}$ | $\\frac{3}{16}$ | $\\frac{1}{4}$ | $\\frac{3}{16}$ | $\\frac{1}{8}$ | $\\frac{1}{16}$ |\n", "\n", "Znalezienie funkcji masy prawdopodobieństwa dla zdefiniowanych wcześniej dyskretnych zmiennych losowych $Y$ oraz $W$ pozostawiamy jako ćwiczenie." ] }, { "cell_type": "markdown", "id": "355992", "metadata": { "collapsed": false }, "source": [ "## Ważne dyskretne rozkłady prawdopodobieństwa\n", "\n", "Poniżej przedstawimy wybrane znane dyskretne rozkłady prawdopodobieństwa, z których będziemy korzystać podczas zajęć.\n", "\n", "**Rozkład dwumianowy / Bernoulliego**\n", "\n", "Jest to rozkład powiązany ze schematem Bernoulliego. Będziemy go wykorzystywać, gdy zmienna losowa $X$ zlicza sukcesy w $n$ próbach Bernoulliego, w których prawdopododobieństwo sukcesu w pojedynczej próbie to $p$. Funkcja masy prawdopodobieństwa zmiennej losowej $X$ o rozkładzie dwumianowym z parametrami $n\\in \\mathbb{N}$ i $p\\in [0,1]$ dana jest wzorem:\n", "\n", "$$\\mathbb{P}(X=k)=\\binom{n}{k}p^k(1-p)^{n-k} \\quad \\text{ dla } \\quad k=0,1,2, \\ldots, n.$$\n", "\n", "Dla zmiennej losowej $X$ o powyższym rozkładzie będziemy stosowali oznaczenie $X\\sim Bin(n,p)$.\n", "\n", "**Rozkład geometryczny** \n", "\n", "Zmienna losowa $X$, która zwraca liczbę prób Bernoulliego potrzebną do otrzymania pierwszego sukcesu (w niezależnych próbach Bernoulliego, gdy prawdopodobieństwo sukcesu w pojedynczej próbie wynosi $p\\in[0,1]$), ma rozkład geometryczny z parametrem $p$. Wówczas jej funkcja masy prawdopodobieństwa dana jest wzorem:\n", "\n", "$$\\mathbb{P}(X=k)=(1-p)^{k-1}p \\quad \\text{ dla } \\quad k=1,2, 3, \\ldots$$\n", "\n", "Dla zmiennej losowej $X$ o powyższym rozkładzie będziemy stosowali oznaczenie $X\\sim Ge(p)$. \n", "\n", "**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", "Dla zmiennej losowej $X$ o powyższym rozkładzie będziemy stosowali oznaczenie $X\\sim Po(\\lambda)$. 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.\n", "\n", "**Rozkład Pascala / ujemny dwumianowy**\n", "\n", "Będziemy mówili, że zmienna losowa $X$ ma rozkład Pascala z parametrami $p\\in [0,1]$ i $r\\in \\mathbb{N}$, jeśli jej funkcja masy prawdopodobieństwa dana jest wzorem:\n", "\n", "$$\\mathbb{P}(X=k)=\\binom{k-1}{r-1}p^r(1-p)^{k-r} \\quad \\text{ dla } \\quad k=r, r+1, r+2, \\ldots$$\n", "\n", "Rozkładu tego używamy, gdy badamy liczbę prób potrzebnych do osiągnięcia $r$-tego sukcesu w niezależnych próbach Bernoulliego, a prawdopodobieństwo sukcesu w pojedynczej próbie wynosi $p$.\n", "\n", "**Rozkład hipegeometryczny**\n", "\n", "Będziemy mówili, że zmienna losowa $X$ ma rozkład hipergeometryczny z parametrami $N, m, n\\in\\mathbb{N}$, gdzie $m\\leq N$ i $n\\leq N$, jeśli jej funkcja masy prawdopodobieństwa dana jest wzorem:\n", "\n", "$$\\mathbb{P}(X=k)=\\frac{\\binom{m}{k}\\binom{N-m}{n-k}}{\\binom{N}{n}} \\quad \\text{ dla } \\quad k=0,1,2,\\ldots, n$$\n", "\n", "Będziemy wówczas stosowali oznaczenie $X\\sim Hip(N, m, n)$. Typowym zastosowaniem tego rozładu jest badanie liczby wylosowanych kul typu A, jeśli losujemy jednocześnie $n$ kul z urny, w której znajduje się $N$ kul, w tym $m$ kul typu A.\n", "\n", "**Przykład 6 (Python)**\n", "\n", "Zdefiniujmy zmienne losowe:\n", "\n", "* $X$ - liczba wylosowanych kierów, gdy losujemy $5$-krotnie, ze zwracaniem jedną kartę z talii $52$ kart,\n", "* $Y$ - liczba wylosowanych kierów, gdy losujemy jednocześnie $5$ kart z talii $52$ kart.\n", "\n", "Wyznaczymy funkcję masy prawdopodobieństwa tych zmienych losowych." ] }, { "cell_type": "code", "execution_count": 9, "id": "72985f", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Funkcja masy prawdopodobieństwa zmiennej losowej X:\n", "-------- -------- -------- --------- --------- -----------\n", "0 1 2 3 4 5\n", "0.237305 0.395508 0.263672 0.0878906 0.0146484 0.000976562\n", "-------- -------- -------- --------- --------- -----------\n" ] }, { "data": { "image/png": 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" ] }, "execution_count": 9, "metadata": { "image/png": { "height": 440, "width": 727 }, "needs_background": "light" }, "output_type": "execute_result" } ], "source": [ "# Zauważmy, że zmienna losowa X ma rozkład dwumianowy, gdzie liczba prób to $n=5$, a prawdopodobieństwo sukcesu (czyli wylosowania kiera) w pojedynczej próbie to p=13/52=1/4\n", "\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import binom\n", "from tabulate import tabulate\n", "\n", "# Parametry rozkładu dwumianowego\n", "\n", "n = 5 # Liczba prób (losowań)\n", "p = 1/4 # Prawdopodobieństwo sukcesu (wylosowania kiera) w pojedynczym losowaniu\n", "\n", "# Wyznaczamy funkcję masy prawdopodobieństwa zmiennej losowej X\n", "\n", "x = range(0, n+1)\n", "pmfX = binom.pmf(x, n, p)\n", "\n", "print('Funkcja masy prawdopodobieństwa zmiennej losowej X:')\n", "print(tabulate([range(0, n+1), pmfX]))\n", "\n", "\n", "# Możemy też przedstawić tę funkcję na wykresie\n", "\n", "plt.bar(x, pmfX)\n", "plt.title('Funkcja masy prawdopodobieństwa zmiennej losowej X')\n", "plt.xlabel('Liczba sukcesów')\n", "plt.ylabel('Prawdopodobieństwo')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "id": "f57d15", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Funkcja masy prawdopodobieństwa zmiennej losowej Y:\n", "-------- ------- ------- --------- --------- -----------\n", "0 1 2 3 4 5\n", "0.221534 0.41142 0.27428 0.0815426 0.0107293 0.000495198\n", "-------- ------- ------- --------- --------- -----------\n" ] }, { "data": { "image/png": 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", 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" ] }, "execution_count": 17, "metadata": { "image/png": { "height": 441, "width": 727 }, "needs_background": "light" }, "output_type": "execute_result" } ], "source": [ "# Zauważmy, że zmienna losowa Y ma rozkład hipergeometryczny, gdzie losujemy n=5 kart z talii N=52 kart, w której m=13 kart to kiery\n", "\n", "from scipy.stats import hypergeom\n", "\n", "# Parametry rozkładu hipergeometrycznego\n", "\n", "N = 52 # Całkowita liczba kart w talii\n", "m = 13 # Liczba kart kierowych\n", "n = 5 # Liczba próbek\n", "\n", "# Wyznaczamy funkcję masy prawdopodobieństwa zmiennej losowej Y\n", "\n", "x = range(0, n+1)\n", "pmfY = hypergeom.pmf(x, N, m, n)\n", "\n", "print('Funkcja masy prawdopodobieństwa zmiennej losowej Y:')\n", "print(tabulate([x, pmfY]))\n", "\n", "# Możemy też przedstawić tę funkcję na wykresie\n", "\n", "plt.bar(x, pmfY)\n", "plt.title('Funkcja masy prawdopodobieństwa zmiennej losowej Y')\n", "plt.xlabel('Liczba wylosowanych kierów')\n", "plt.ylabel('Prawdopodobieństwo')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7d7a7a", "metadata": { "collapsed": false }, "source": [ "## Dystrybuanta zmiennej losowej\n", "\n", "Innym sposobem definiowania rozkładu prawdopodobieństwa zmiennej losowej jest zastosowanie tzw. dystrybuanty, która dla każdego $x\\in\\mathbb{R}$ zwraca ,,skumulowane\" prawdopodobieństwo, czyli w tym wypadku prawdopodobieństwo tego, że zmienna losowa trafia w nieskończony przedział $(-\\infty, x]$.\n", "\n", "**Definicja (dystrybuanta)**\n", "\n", "**Dystrybuantą** zmiennej losowej $X$ nazywamy funkcję $F_{X}:\\mathbb{R}\\to[0,1]$ daną wzorem:\n", "\n", "$$ F_{X}(x)=\\mathbb{P}(X\\le x) = \\mathbb{P}(X^{-1}\\left((-\\infty,x]\\right)). $$\n", "\n", "W szczególności dla zmiennej losowej dyskretnej o zbiorze atomów $A=\\{a_1,a_2,\\ldots\\}$ mamy:\n", "\n", "$$F_{X}(x)=\\sum_{a\\in A, a\\le x}\\mathbb{P}(X=a). $$\n", "\n", "**Przykład 6**\n", "\n", "Wyznaczymy dystrybuantę zmiennej losowej $X$ zdefiniowanej w przykładzie 1. Przypomnijmy, że jest to zmienna losowa dyskretna, która zwraca sumę oczek w dwóch rzutach czworościenną kostką. Funkcję masy prawdopodobieństwa tej zmiennej losowej wyznaczyliśmy w przykładzie 5:\n", "\n", "| $k$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |\n", "| --- | --- | --- | --- | --- | --- | --- | --- |\n", "| $\\mathbb{P}(X=k)$ | $\\frac{1}{16}$ | $\\frac{1}{8}$ | $\\frac{3}{16}$ | $\\frac{1}{4}$ | $\\frac{3}{16}$ | $\\frac{1}{8}$ | $\\frac{1}{16}$ |\n", "\n", "Wyznaczymy teraz wzór dystrybuanty tej zmiennej losowej. Zacznijmy wpierw od rozważenia argumentów $x<2$. Wówczas:\n", "\n", "$$\\forall_{x<2}\\, F_{X}(x)=\\mathbb{P}(X\\le x) = \\mathbb{P}(\\emptyset)=0,$$\n", "\n", "bo nie ma zdarzeń elementarnych, dla których zmienna losowa $X$ osiągałaby wartość mniejszą od $2$. \n", "\n", "Następnie rozważymy argumenty $x$ z przedziału $[2,3)$:\n", "\n", "$$\\forall_{x\\in [2,3)}\\, F_{X}(x)=\\mathbb{P}(X\\le x)=\\mathbb{P}(\\{(1,1)\\})=\\frac{1}{16}.$$\n", "\n", "Alternatywnie, możemy zsumować prawdopodobieństwa wszystkich atomów mniejszych lub równych od argumentu $x$, co w tym przypadku oznacza po prostu prawdopodobieństwo jednego atomu 2:\n", "\n", "$$\\forall_{x\\in [2,3)}\\, F_{X}(x)=\\mathbb{P}(X\\le x) = \\mathbb{P}(X=2)=\\frac{1}{16}.$$\n", "\n", "Kolejny przedział argumentów, które powinniśmy rozważyć to przedział $[3,4)$:\n", "\n", "$$\\forall_{x\\in [3,4)}\\, F_{X}(x)=\\mathbb{P}(X\\le x)=\\mathbb{P}(\\{(1,1), (1,2), (2,1)\\})=\\frac{3}{16}.$$\n", "\n", "Alternatywnie, możemy to też obliczyć używając bezpośrednio funkcji masy prawdopodobieństwa:\n", "\n", "$$\\forall_{x\\in [3,4)}\\, F_{X}(x)=\\mathbb{P}(X\\le x) = \\mathbb{P}(X=2)+\\mathbb{P}(X=3)=\\frac{1}{16}+\\frac{1}{8}=\\frac{3}{16}.$$\n", "\n", "W analogiczny sposób obliczamy wzór dystrybuanty dla pozostałych argumentów, otrzymując ostatecznie:\n", "\n", "$$ F_X(x)=\\begin{cases} 0, &\\text{ dla } x<2;\\\\\n", "\\frac{1}{16}, &\\text{ dla } 2\\leq x <3;\\\\\n", "\\frac{3}{16}, &\\text{ dla } 3\\leq x <4;\\\\\n", "\\frac{3}{8}, &\\text{ dla } 4\\leq x<5;\\\\\n", "\\frac{5}{8}, &\\text{ dla } 5\\leq x<6;\\\\\n", "\\frac{13}{16}, &\\text{ dla } 6\\leq x<7;\\\\\n", "\\frac{15}{16}, &\\text{ dla } 7\\leq x<8;\\\\\n", "1, &\\text{ dla } x\\geq 8.\\end{cases}$$\n", "\n", "Możemy też narysować wykres dystrybuanty tej zmiennej losowej. W przypadku dystrybuanty zmiennej losowej dyskretnej wykres ten będzie przedstawiała tzw. **funkcja schodkowa**, w której ,,skoki'' występują dla argumentów będących atomami tej zmiennej losowej, a wysokości poszczególnych schodków odpowiadają prawdopodobieństwom odpowiednich atomów." ] }, { "cell_type": "code", "execution_count": 18, "id": "ba96dd", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 18, "metadata": { "image/png": { "height": 440, "width": 720 }, "needs_background": "light" }, "output_type": "execute_result" } ], "source": [ "# Definiujemy miejsca schodków i wysokości, na jakich się znajdują\n", "\n", "steps = [0, 1/16, 3/16, 3/8, 5/8, 13/16, 15/16, 1]\n", "x = range(1, 10)\n", "\n", "# Rysujemy poziome linie odpowiadające wartościom dystrybuanty\n", "\n", "for i in range(len(x) - 1):\n", " plt.hlines(steps[i], x[i], x[i+1], color='b', linewidth=2)\n", "\n", "# Dorysowujemy zamalowane i puste kółeczka, aby było jasne, jakie są wartości dystrybuanty w miejscu ,,skoków''\n", "\n", "plt.plot(range(2, 9), steps[0:7], 'bo', fillstyle='none')\n", "plt.plot(range(2, 9), steps[1:8], 'bo')\n", "\n", "\n", "# Dodajemy nazwy osi i tytuł wykresu\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('F_X(x)')\n", "plt.title('Dystrybuanta zmiennej losowej X')\n", "\n", "\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "57ad8d", "metadata": { "collapsed": false }, "source": [ "## Wartość oczekiwana zmiennej losowej\n", "\n", "Ze zmiennymi losowymi wiążą się różne parametry liczbowe, które pomagają nam badać zachowanie tych zmiennych losowych. Jednym z podstawowych parametrów jest tzw. ,,wartość oczekiwana''. Intuicyjnie można powiedzieć, że jest to wartość średnia, którą przyjmuje dana zmienna losowa.\n", "\n", "**Definicja (wartość oczekiwana zmiennej losowej dyskretnej)**\n", "\n", "**Wartością oczekiwaną** (lub **wartością średnią**) dyskretnej zmiennej losowej $X$ o zbiorze atomów $A=\\{a_1,a_2,\\ldots\\}$ nazywamy liczbę\n", "\n", "$$ \\mathbb{E} {X}=\\sum_{a_i\\in A} a_i \\mathbb{P}(X= a_i),$$\n", "\n", "o ile suma szeregu po prawej stronie powyższego równania istnieje. Jeśli szereg po prawej stronie powyższego równania nie jest bezwględnie zbieżny, mówimy, że wartość oczekiwana zmiennej losowej X nie istnieje.\n", "\n", "**Przykład 7**\n", "\n", "Obliczymy wartość oczekiwaną zmiennej losowej $X$ zdefiniowanej w przykładzie 1. Przypomnijmy, że funkcja masy prawdopodobieństwa tej zmiennej losowej to:\n", "\n", "| $k$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |\n", "| --- | --- | --- | --- | --- | --- | --- | --- |\n", "| $\\mathbb{P}(X=k)$ | $\\frac{1}{16}$ | $\\frac{1}{8}$ | $\\frac{3}{16}$ | $\\frac{1}{4}$ | $\\frac{3}{16}$ | $\\frac{1}{8}$ | $\\frac{1}{16}$ |\n", "\n", "Zatem wartość oczekiwana tej zmiennej losowej to:\n", "\n", "\\begin{align*}\n", "\\mathbb{E}(X)&=2\\cdot \\mathbb{P}(X=2)+3\\cdot \\mathbb{P}(X=3)+4\\cdot \\mathbb{P}(X=4)+5\\cdot \\mathbb{P}(X=5)+6\\cdot \\mathbb{P}(X=6)+7\\cdot \\mathbb{P}(X=7)+8\\cdot \\mathbb{P}(X=8)\\\\\n", "&=2\\cdot\\frac{1}{16}+3\\cdot\\frac{1}{8}+4\\cdot\\frac{3}{16}+5\\cdot\\frac{1}{4}+6\\cdot\\frac{3}{16}+7\\cdot\\frac{1}{8}+8\\cdot\\frac{1}{16}=5.\n", "\\end{align*}\n", "\n", "W przypadku zmiennych losowych o jednym z ważnych rozkładów prawdopodobieństwa mamy gotowe wzory pozwalające obliczyć wartość oczekiwaną.\n", "\n", "| Rozkład zmiennej losowej $X$ | Parametry | $\\mathbb{E}(X)$ |\n", "| --- | --- | --- |\n", "| dwumianowy | $n, p$ | $np$ |\n", "| geometryczny | $p$ | $\\frac{1}{p}$ |\n", "| Poissona | $\\lambda$ | $\\lambda$ |\n", "| Pascala | $p, r $ | $\\frac{r}{p}$ |\n", "| hipergeometryczny | $N, m, n$ | $\\frac{nm}{N}$ |\n", "\n" ] } ], "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" } }, "nbformat": 4, "nbformat_minor": 4 }