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author | enezerdem <105669082+enezerdem@users.noreply.github.com> | 2022-06-01 14:34:01 +0200 |
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committer | GitHub <noreply@github.com> | 2022-06-01 14:34:01 +0200 |
commit | 50030d5cc2bb12208ad64dd4f4730d2d71edf3a3 (patch) | |
tree | aeffdfd06e1eec43070a58cee09b7e436792ee28 /vorlesungen/slides/dreieck/beta.tex | |
parent | Merge pull request #7 from AndreasFMueller/master (diff) | |
parent | fix participant lists (diff) | |
download | SeminarSpezielleFunktionen-50030d5cc2bb12208ad64dd4f4730d2d71edf3a3.tar.gz SeminarSpezielleFunktionen-50030d5cc2bb12208ad64dd4f4730d2d71edf3a3.zip |
Merge pull request #8 from AndreasFMueller/master
synch
Diffstat (limited to 'vorlesungen/slides/dreieck/beta.tex')
-rw-r--r-- | vorlesungen/slides/dreieck/beta.tex | 70 |
1 files changed, 70 insertions, 0 deletions
diff --git a/vorlesungen/slides/dreieck/beta.tex b/vorlesungen/slides/dreieck/beta.tex new file mode 100644 index 0000000..fc3606a --- /dev/null +++ b/vorlesungen/slides/dreieck/beta.tex @@ -0,0 +1,70 @@ +% +% beta.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Beta-Verteilung} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.40\textwidth} +\begin{block}{Ordnungsstatistik} +\begin{align*} +\varphi(x) +&= +{\color{blue}N} x^{k-1} (1-x)^{n-k} +\\ +&\uncover<8->{ += +\beta_{k,n-k+1}(x) +} +\end{align*} +\end{block} +\uncover<8->{% +\begin{block}{Risch-Algorithmus} +Die Beta-Verteilungen haben ausser in Spezialfällen +keine Stammfunktion in geschlossener Form. +\end{block}} +\end{column} +\begin{column}{0.56\textwidth} +\uncover<2->{% +\begin{definition} +Beta-Verteilung +\[ +\beta_{a,b}(x) += +\begin{cases} +\displaystyle +\uncover<7->{ +{\color{blue} +\frac{1}{B(a,b)} +} +} +x^{a-1}(1-x)^{b-1} +&0\le x\le 1 +\\ +0&\text{sonst} +\end{cases} +\] +\end{definition}} +\uncover<3->{% +\begin{block}{Normierung} +\begin{align*} +{\color{blue}\frac{1}{{N}}} +&\uncover<4->{= +\int_{-\infty}^\infty \beta_{a,b}(x)\,dx} +\\ +&\uncover<5->{= +\int_{0}^1 x^{a-1}(1-x)^{b-1}\,dx} +\\ +&\uncover<6->{= +B(a,b)} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |