From 63cef30364f2b9339fbf1320cab26298f822c179 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Wed, 26 Feb 2025 18:22:35 +0100 Subject: [PATCH] gramatika --- nahodne-veliciny.tex | 4 ++-- skripta.pdf | Bin 121115 -> 121118 bytes 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/nahodne-veliciny.tex b/nahodne-veliciny.tex index efa6191..eeb4b6f 100644 --- a/nahodne-veliciny.tex +++ b/nahodne-veliciny.tex @@ -148,7 +148,7 @@ Příkladem singulární distribuční funkce je například integrál takzvané Náhodnou veličinu $X$ nazveme \textit{diskrétní}, jestliže existují $\emptyset \neq I \subset \mathbb{N}$, $\{x_i\}_{i \in I}$ a $\{p_i \in (0,1]\}_{i \in I}$ takové že $P[X \in B] = \sum_{i, x_i \in B} p_i$ pro všechny borelovské $B$. \end{definition} -Platí $P[X = x_i] = p_i$ a $\sum_{i \in I} p_i = 1$. Rozdělením takové veličiny je funkce $P_X = \sum_{i \in I} p_i \delta_{x_i}$, kde $\delta_u$ je Diracova míra v bodě $u$. Toto rozdělení je spojité vůči čítací míře na $S = \{x_i\}_{i \in I} \subset \mathbb{R}$. Potom funkce +Platí $P[X = x_i] = p_i$ a $\sum_{i \in I} p_i = 1$. Rozdělením takové veličiny je funkce $P_X = \sum_{i \in I} p_i \delta_{x_i}$, kde $\delta_u$ je Diracova míra v bodě $u$. Toto rozdělení je absolutně spojité vůči čítací míře na $S = \{x_i\}_{i \in I} \subset \mathbb{R}$. Potom funkce $f_X(u) := \begin{cases} p_i, u = x_i,\\ 0, \text{jinak} @@ -158,7 +158,7 @@ $f_X(u) := \begin{cases} Náhodná veličina $X$ se nazývá \textit{(absolutně) spojitá}, pokud její rozdělení $P_X$ je absolutně spojité vůči Lebesgueově míře $\lambda$. \end{definition} -Pro spojitou náhodnou veličinu $X$ vždy existuje hustota $f_X$ (nezáporná a jednoznačná až na množinu $\lambda$-míry $0$) splňující $P[X\in B] = \int_B f_X(t) dt$ a speciálně $F_X(a) = \int_{-\infty}^a f_X(t) dt$ pro všechna $a \in \mathbb{R}$. Taková $F_X$ má derivaci ve skoro všech bodech a platí $F'_X(a) = f_X(a)$ pro s.v. $a$. Analogicky pro diskrétní náhodnou veličinu $Y$ je hustota funkcí, která nabývá v bodě $a$ hodnotu distribuční funkce v daném bodě. +Pro spojitou náhodnou veličinu $X$ vždy existuje hustota $f_X$ (nezáporná a jednoznačná až na množinu $\lambda$-míry $0$) splňující $P[X\in B] = \int_B f_X(t) dt$ a speciálně $F_X(a) = \int_{-\infty}^a f_X(t) dt$ pro všechna $a \in \mathbb{R}$. Taková $F_X$ má derivaci ve skoro všech bodech a platí $F'_X(a) = f_X(a)$ pro s.v. $a$. Analogicky pro diskrétní náhodnou veličinu $Y$ je hustota funkcí, která nabývá v bodě $a$ hodnoty distribuční funkce v daném bodě. Ne každá veličina, se kterou se běžně setkáme je ryze spojitá nebo ryze diskrétní. Příkladem veličiny, která má obě složky nenulové, je například úhrn denních srážek, s nenulovou pravděpodobností nenaprší vůbec, ale když už začne pršet, úhrn srážek je spojitá náhodná veličina. diff --git a/skripta.pdf b/skripta.pdf index 7b6662b2dec25ad722e1678fcbf27aa55b217fe3..1c795e5e74e2e46a0013433c5658adabc65d4833 100644 GIT binary patch delta 10305 zcmaiaQ*ho7uy)eeHX7TujmEZZ^Vb+}&<1a8H@4Z>w%H_2W9$2WGw0&motwSdnVr3P zb{}Llz~wf;)iI|5oFXEK9-i)2W=@E{>lcQKiNviKJtsO!&Ykd?j)ba_ud9uMx0aN|I`?Jam z-}r^P_H9IOdPPZk{Jo#vSFZbZ_*^}GAAGOA`9VcTjfLC*3B;tiIX#^V>xIkMO+0A& zo#pY|k287i5oJWZ*=U26e6dQoCtGj#Ey(U$6yvY>h6J};7YyXaTgmhmA3X{q-`(YO z;ey%~M)4yKiDW++!^FO3$C5(95Ll&x@clMq)Tof{{)+18NJk9A1n4FN1`8H&8W3Lv zqX-!AJw4(AaO)7yUZ^je>ahK<)KEU|Y)4{!OmJ{VMR5D_hvFJO3{Y?~j1JlLlcCy& zo`3ux{>X$O()coEg;pyUAc>@i1I9Rs8s8(M5r)yfbhpI4Xzbe!udn9Jr#+`kW~#<( zz>}xEM-N23B0!CI%6`~1Jyd=4U4H%ANKbZkF0T{w`~e2mt~e3N))|g!-2h| z+`1)I1q}yF%(_S1nX7(rUFArRW7b%L?6v6`0QNDSeMGshR(H2;6?`gURsF5 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