From c7fe40167f628dc05035423e5d1d94ae85345aef Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Mon, 24 Feb 2025 16:24:44 +0100 Subject: [PATCH] chybejici zavorky --- nahodne-jevy.tex | 2 +- skripta.pdf | Bin 106578 -> 106581 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/nahodne-jevy.tex b/nahodne-jevy.tex index 1d5952f..c1a9bb9 100644 --- a/nahodne-jevy.tex +++ b/nahodne-jevy.tex @@ -190,7 +190,7 @@ Použití Bayesovy věty si ukážeme na následujícím příkladu. \end{example} \begin{theorem}{\textbf{(O postupném podmiňování)}} - Nechť ${A_i}_{i=1}^n$ jsou náhodné jevy takové, že $P(\bigcap_{i=1}^n) > 0$. Pak platí + Nechť $\{A_i\}_{i=1}^n$ jsou náhodné jevy takové, že $P(\bigcap_{i=1}^n) > 0$. Pak platí $$ P(\bigcap_{i=1}^n A_i ) = P(A_n | \bigcap_{i=1}^{n-1}) \cdot P(A_2|A_1) \cdot P(A_1). $$ \begin{proof} Dokazujeme indukcí podle počtu náhodných jevů. Z definice podmíněné pravděpodobnosti víme, že $P(A_2 \cap A_1) = P(A_2 | A_1) P(A_1)$. 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