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author | Samuel Niederer <43746162+samnied@users.noreply.github.com> | 2022-07-24 12:17:00 +0200 |
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committer | GitHub <noreply@github.com> | 2022-07-24 12:17:00 +0200 |
commit | efe7c35759afb5cbae3c1683873c5159be0be09f (patch) | |
tree | 84f2e8510132352f9943bddc577ccf32cd46f2dc /vorlesungen/slides/dreieck/stichprobe.tex | |
parent | add current work (diff) | |
parent | Merge pull request #26 from p1mueller/master (diff) | |
download | SeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.tar.gz SeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.zip |
Merge branch 'AndreasFMueller:master' into master
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-rw-r--r-- | vorlesungen/slides/dreieck/stichprobe.tex | 64 |
1 files changed, 64 insertions, 0 deletions
diff --git a/vorlesungen/slides/dreieck/stichprobe.tex b/vorlesungen/slides/dreieck/stichprobe.tex new file mode 100644 index 0000000..4b2eff0 --- /dev/null +++ b/vorlesungen/slides/dreieck/stichprobe.tex @@ -0,0 +1,64 @@ +% +% 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 $X$ \uncover<5->{mit +Verteilungsfunktion +\[ +F_X(x) += +P(X\le x) +\]} +\uncover<6->{und +Wahrscheinlichkeitsdichte +\[ +\varphi_X(x) += +\frac{d}{dx} F_X(x) +\]} +\end{block} +\uncover<7->{% +\begin{block}{Gleichverteilung} +\[ +F(x) = \begin{cases} +0&\qquad x<0\\ +x&\qquad 0\le x \le 1\\ +1&\qquad 1<x +\end{cases} +\uncover<8->{ +\qquad\Rightarrow\qquad +\varphi(x) += +\begin{cases} +1&\qquad 0\le x \le 1\\ +0&\qquad\text{sonst}. +\end{cases} +} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<2->{% +\begin{block}{Stichprobe} +$n$ Zufallsvariablen $X_1,\dots,X_n$ +\begin{itemize} +\item<3-> +alle $X_i$ haben die gleiche Verteilung wie $X$ +\item<4-> +die $X_i$ sind unabhängig +\end{itemize} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |