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z?nz+UMDlZfZ9ez+rJyyiD%KG%a*zKzIcl(Pn`qzYP~Ucwd}G`C#{JR2i{IQVw5FMOw>J3Aok(k% zi&vTNH}~H*EyR1k|NMQ5H7&*aVW#DO_ToMM%W|Z6zhqgC59V^qt;G9hxaEXkuCN>> z-hZzwCyV!HhUL~02$Wdv8qBXPw~;`-KP`8cKv=Hjwh~BcX}M=Gms*aNK*q0@( diff --git a/stredni-hodnota.tex b/stredni-hodnota.tex index 80a3977..ec023d1 100644 --- a/stredni-hodnota.tex +++ b/stredni-hodnota.tex @@ -363,7 +363,7 @@ Následující věta nám umožňuje jednoznačně popisovat rozdělení jak pod Potom $$ \frac{1}{\pi} \left[\int_0^T \frac{\sin(t(x - a))}{t} dt - \int_0^T \frac{\sin(t(x - b))}{t} dt \right] \overset{T \rightarrow \infty}\rightarrow \begin{cases} \frac{1}{2}, x = a, b \\ - 1, a < x < b, + 1, a < x < b, \\ 0, \text{jinak}. \end{cases}$$ Dosazením do předchozího vzorce a užitím Lebesgueovy věty o konvergentní majorantě dostáváme @@ -376,7 +376,7 @@ Z předchozí věty okamžitě plyne následující důsledek. Platí $\varphi_X = \varphi_Y \Leftrightarrow X \overset{d}{=} Y$. \end{corollary} -Nakonec definujeme charakteristickou funkci pro náhodné vektory. Obdobným způsobem pro ní můžeme dokázat vlastnosti, které platí pro jednorozměrné náhodné veličiny. +Nakonec definujeme charakteristickou funkci pro náhodné vektory. Obdobným způsobem pro ní můžeme dokázat vlastnosti, které jsme již dokázali pro jednorozměrné náhodné veličiny. \begin{definition} \textit{Charakteristická funkce} náhodného vektoru $\vec{X} = [X_1, \dots, X_d]^T$ je definována vztahem