From eff2374ac1568e74587f025897f2a656746848ba Mon Sep 17 00:00:00 2001 From: Christian Bay Date: Thu, 1 Oct 2015 16:27:52 +0200 Subject: [PATCH] Exponentialfunktion: Dichte und Verteilung + Wertebereich --- Public/m4/MaC4Cheatsheet.tex | 16 ++++++++++++++-- 1 file changed, 14 insertions(+), 2 deletions(-) diff --git a/Public/m4/MaC4Cheatsheet.tex b/Public/m4/MaC4Cheatsheet.tex index afbdfbe..684cf51 100644 --- a/Public/m4/MaC4Cheatsheet.tex +++ b/Public/m4/MaC4Cheatsheet.tex @@ -286,8 +286,20 @@ $f(x) = \frac{1}{\sqrt{2\pi}}*e^{-0.5x^2}$ $f(x) = N(\mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}*e^{-\frac{1}{2\sigma^2}(x- \mu)^2} \quad \quad m_1 = \mu \quad \quad \widehat{m}_2=\sigma^2$ \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} Zufallsexperimente, bei denen jedes Ergebnis die gleiche Chance hat. \\ $f(w) = L(\Omega) = \frac{1}{|\Omega|}$