From d2ea0ce2de87195e213b71abcc2b0f296b4db409 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Sun, 16 Mar 2025 11:25:30 +0100 Subject: [PATCH] oprava preklepu --- nahodne-veliciny.tex | 2 +- skripta.pdf | Bin 194843 -> 194846 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/nahodne-veliciny.tex b/nahodne-veliciny.tex index a67af69..8318639 100644 --- a/nahodne-veliciny.tex +++ b/nahodne-veliciny.tex @@ -567,7 +567,7 @@ $$ P[Y = y] = P[t(X) = y] = P[X \in t^{-1}(y)] = \sum_{t(x) = y} P[X = x]. $$ Dále mějme spojitou náhodnou veličinu $X$, známe její hustotu $f_X(x)$. Cílem je spočítat hustotu $f_Y(y)$, kde $Y = t(X)$. Pro každé $y$ můžeme nalézt množinu $\mathcal{T}_y = \{x: t(x) \leq y\}$. Poté můžeme spočítat distribuční funkci rozdělení $Y$. $$ F_Y(y) = P[Y \leq y] = P[t(X) \leq Y] = P[\omega: t(X(\omega)) \leq Y] = \int_{\mathcal{T}(y)} f_X(x) dx, $$ -hustotu poté můžeme získat pouhým zderivování distribuční funkce $F_y$. +hustotu poté můžeme získat pouhým zderivováním distribuční funkce $F_y$. Dále uvažujme případ (dvourozměrného) diskrétního náhodného vektoru $[X, Y]^T$ a transformace $Z = t(X, Y)$. Ze znalosti diskrétního rozdělení vektoru $[X, Y]$ chceme spočítat $P[Z = z]$. Můžeme psát $$ P[Z = z] = P[t(X, Y) = z] = P[\omega: t([X, Y]^T(\omega)) = z] = $$ diff --git a/skripta.pdf b/skripta.pdf index b74e6bbba5cfc8997f7849a5038bb3fddd2dcaab..b981872df6510a2d36905e9e6b3211de2346dbbd 100644 GIT binary patch delta 6234 zcmV-g7^UZ%@(Z5w3xKo%+g<@Om)u?fDSueY_F<*j*;5Xw%E9)p4@frqHRPygGLo%b z+vS=^W7urq1MmTayZ?01Y55DC$Ie4gA^zze|1IDBCjb7{{pGIv^H1PAxkN~|yW4jJ z$`c#k^@Q@ylIiYt@2~!G{qgSaQJCh!UU?swWUVOkzQ`;VjH`GHgUq|?I-o_!fqxx@ z-c}b9AqS*+5c*tQ$tkoD%0eHD3^aFiqqXDP-WVhA>@ONAXk^yfpnQIaujQ(|YYpzG{TkDb1PBRX&mwLkgR@X7g1;ODU^WmzxkWuWdfHn*L zTwN$AZJa9``fz>p3B3a6{kN{M@qa;iaWhaX7!HFFRu>A&>HuriBX*>MH*9&Xd#eD9 z%X$;=mj%N@m=q#WQ5jSp(JD(pR_f;~ZZYW=3w*d<*#MVrZxw^acoR$3`Gp2iFP=sA z$1DaDR~BU&8QzE$S!^oI~u{VAl?o!AAil4w_pLG z0$-w+T44e40j;-8VgWV*e<;bc!sVz)qjoadDY1twE_VtQ_}t)dp4l&`z(h%ef(Vlj zmfbeKQonQAO@%s%_Ha&Du8(LvG!}{xK^sw(+CIa39x6)soA~oYX%Q*fU;M zT0@jgk*b*7+>w7&?lU(@L`Ia3lF>ZHfTbmrpW$euXu3(+>Y`ahe=~IJd8xGUydH!( zTNBom(zZsQ1iY&^*FBJLL|oJ=NZeWV>Q)dbs~Sb%3@w8vtfIVBYA7spCY$Vg+gnJj zxB=>^o*ddB5!giy(Nf92ZD3Q7;HGWqRNlARnMA=q(asc&N)|DfPt7MP{)85RFsg_o zpB*GCwR8eYkzT@Ee*!L+-<$&P!B|h1Hf28zWLuqs0}v`CsQ?dx!x8L51Rjo*{8=Ht zRJ@Q2wqe$=dKeyWUyylrC0ct1kBWiD{CX+Mdf)1oA!|0LH2S|ZSb_F{{I!m2dyou= zfX1eSo&b?LzGnTs>MHT{h_}7+|5nxavNd6SN4d!6XG;0Af0N$3Mwy5{_FGRr6W&~P z9xe|HlmN>k``^V#!4_LTHB!KWp5S29 zNCC_Ktik6SDR|RpA_!dqZ^tvRjbjC08esGe$$#@>1<66E?I6s={A}Z9XACMh$yXp? 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