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Erwartungswerte der Verteilungen

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Daniel Thiem 2012-09-26 12:49:49 +02:00
parent 0b7b594a3e
commit 969997a529
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@ -23,7 +23,7 @@
\title{Stochastische Signale und Systeme}
\subtitle{Zusammenfassung Formeln}
\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.9.7.2 - 26.09.2012}
\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.9.8 - 26.09.2012}
\maketitle
\newpage
@ -107,6 +107,13 @@ P(X>a)&=1-F(a)
\begin{equation}
f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{1}{2} \left(\frac{t-\mu}{\sigma}\right)^2}
\end{equation}
Erwartungswert und Varianz:
\begin{subequations}
\begin{align}
\E[f(x)]&=\mu \\
\Var[f(x)]&=\sigma^2
\end{align}
\end{subequations}
\subsection{Rechteckverteilung}
\begin{align}
@ -120,6 +127,13 @@ F(x) &= \begin{cases}
1 & x > b
\end{cases}
\end{align}
Erwartungswert und Varianz:
\begin{subequations}
\begin{align}
\E[f(x)]&=\frac{a+b}{2} \\
\Var[f(x)]&=\frac{(b-a)^2}{12}
\end{align}
\end{subequations}
\subsection{Exponentialverteilung}
\begin{align}
@ -132,6 +146,13 @@ F(x) &= \begin{cases}
1-e^{-\lambda t} & x\geq 0
\end{cases}
\end{align}
Erwartungswert und Varianz:
\begin{subequations}
\begin{align}
\E[f(x)]&=\frac{1}{\lambda} \\
\Var[f(x)]&=\frac{1}{\lambda^2}
\end{align}
\end{subequations}
\section{Formel von Bayes}