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author | LordMcFungus <mceagle117@gmail.com> | 2022-03-14 16:40:46 +0100 |
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committer | GitHub <noreply@github.com> | 2022-03-14 16:40:46 +0100 |
commit | 3e436682e822f424ddad2b6d908c464b4e645b07 (patch) | |
tree | 063fb8248cf0e95529c260df130297871dd4d3bf /vorlesungen/slides/dreieck/stichprobe.tex | |
parent | Name und Titel (diff) | |
parent | move command configuration to common/Makefile.inc (diff) | |
download | SeminarSpezielleFunktionen-3e436682e822f424ddad2b6d908c464b4e645b07.tar.gz SeminarSpezielleFunktionen-3e436682e822f424ddad2b6d908c464b4e645b07.zip |
Merge pull request #2 from AndreasFMueller/master
update
Diffstat (limited to 'vorlesungen/slides/dreieck/stichprobe.tex')
-rw-r--r-- | vorlesungen/slides/dreieck/stichprobe.tex | 60 |
1 files changed, 60 insertions, 0 deletions
diff --git a/vorlesungen/slides/dreieck/stichprobe.tex b/vorlesungen/slides/dreieck/stichprobe.tex new file mode 100644 index 0000000..da3a20e --- /dev/null +++ b/vorlesungen/slides/dreieck/stichprobe.tex @@ -0,0 +1,60 @@ +% +% stichprobe.tex -- Stichprobe +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Stichprobe} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Zufallsvariable} +Gegeben eine Zufallsvariable $X$ mit +Verteilungsfunktion +\[ +F_X(x) += +P(X\le x) +\] +und +Wahrscheinlichkeitsdichte +\[ +\varphi_X(x) += +\frac{d}{dx} F_X(x) +\] +\end{block} +\begin{block}{Gleichverteilung} +\[ +F(x) = \begin{cases} +0&\qquad x<0\\ +x&\qquad 0\le x \le 1\\ +1&\qquad 1<x +\end{cases} +\qquad\Rightarrow\qquad +\varphi(x) += +\begin{cases} +1&\qquad 0\le x \le 1\\ +0&\qquad\text{sonst}. +\end{cases} +\] +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Stichprobe} +$n$ Zufallsvariablen $X_1,\dots,X_n$ +\begin{itemize} +\item +alle $X_i$ haben die gleiche Verteilung wie $X$ +\item +die $X_i$ sind unabhängig +\end{itemize} +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup |