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Exponentialfunktion: Dichte und Verteilung + Wertebereich

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Christian Bay 2015-10-01 16:27:52 +02:00
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Public/m4/MaC4Cheatsheet.tex
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@ -286,8 +286,20 @@ $f(x) = \frac{1}{\sqrt{2\pi}}*e^{-0.5x^2}$
$f(x) = N(\mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}*e^{-\frac{1}{2\sigma^2}(x- $f(x) = N(\mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}*e^{-\frac{1}{2\sigma^2}(x-
\mu)^2} \quad \quad m_1 = \mu \quad \quad \widehat{m}_2=\sigma^2$ \mu)^2} \quad \quad m_1 = \mu \quad \quad \widehat{m}_2=\sigma^2$
\subsection{Exponentiallverteilung} \subsection{Exponentiallverteilung}
$f(\lambda) = \lambda*e^{-\lambda t}$ \textbf{Dichtefunktion}:
\begin{align} f_\lambda(x) =
\begin{cases}
\lambda*e^{-\lambda x} & x \geq 0 \\
0 & x < 0
\end{cases}
\end{align}
\textbf{Verteilungsfunktion}:
\begin{align} F(x) = \int_0^x f_\lambda(t) dt =
\begin{cases}
1 - e^{-\lambda x} & x \geq 0 \\
0 & x < 0
\end{cases}
\end{align}
\subsection{Laplace-Verteilung} \subsection{Laplace-Verteilung}
Zufallsexperimente, bei denen jedes Ergebnis die gleiche Chance hat. \\ Zufallsexperimente, bei denen jedes Ergebnis die gleiche Chance hat. \\
$f(w) = L(\Omega) = \frac{1}{|\Omega|}$ $f(w) = L(\Omega) = \frac{1}{|\Omega|}$