From bd72cad8a12f017902eb5147c26e3c76f235e713 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Tue, 25 Feb 2025 17:59:59 +0100 Subject: [PATCH] stylisticke upravy --- nahodne-veliciny.tex | 5 +++-- skripta.pdf | Bin 121103 -> 121115 bytes 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/nahodne-veliciny.tex b/nahodne-veliciny.tex index e5ada0a..efa6191 100644 --- a/nahodne-veliciny.tex +++ b/nahodne-veliciny.tex @@ -103,7 +103,7 @@ Uvedeme si několik užitečných vlastností distribučních funkcí: \end{cases} $$ - Dále, z toho že $P_Y({0}) = \frac{1}{4} > 0$, naše míra není absolutně spojitá vůči Lebesgueově míře $\lambda$, musíme uvažovat čítací míru $\mu_\mathbb{Z}$ na množině celých čísel. Potom hustota $f_Y$ má následující tvar: + Dále, z toho, že $P_Y({0}) = \frac{1}{4} > 0$, plyne, že míra $P_Y$ není absolutně spojitá vůči Lebesgueově míře $\lambda$, tedy musíme uvažovat čítací míru $\mu_\mathbb{Z}$ na množině celých čísel. Potom hustota $f_Y$ má následující tvar: $$ f_Y(a) = \begin{cases} \frac{1}{4}, a = 0,\\ @@ -124,7 +124,7 @@ Vidíme, že hustota odpovídá skokům distribuční funkce v daném bodě. V n \item $F_X$ je zprava spojitá. \end{enumerate} - Dále, každá funkce $F$ splňující body (i)-(iii) z této věty je distribuční funkcí nějaké náhodné veličiny. + Navíc, každá funkce $F$ splňující body (i)-(iii) z této věty je distribuční funkcí nějaké náhodné veličiny. \begin{proof} Dokážeme pouze implikaci o vlastnostech distribuční funkce, opačná implikace (existuje rozdělení) vyžaduje pokročilý matematický aparát z analýzy a teorie míry, který prozatím postrádáme. @@ -178,3 +178,4 @@ Ne každá veličina, se kterou se běžně setkáme je ryze spojitá nebo ryze \end{lemma} \hfill \textit{konec 4. přednášky (25.2.2025)} + diff --git a/skripta.pdf b/skripta.pdf index ac090d598d026a5f8ee084a693cbb25352e75010..7b6662b2dec25ad722e1678fcbf27aa55b217fe3 100644 GIT binary patch delta 11077 zcmajlLwp<#fCb=2O=H`(&1u-!wynmVsIhIcu|2VE+YKjn_P@8i?fqT8&vxOtsJDqhGl>?XOM1F%2tg*?5Y zR^U3KZ+)Zxa2hZjH+%i6ohU~-QuV*9Dm!_%&Q8d=NdTs36G#Z|I}tIto;oXiG2Yu@ 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