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author | Nicolas Tobler <nicolas.tobler@ost.ch> | 2022-08-03 20:37:12 +0200 |
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committer | Nicolas Tobler <nicolas.tobler@ost.ch> | 2022-08-03 20:37:12 +0200 |
commit | e08392d4bacb9a54c3ab755fa6445514749b608f (patch) | |
tree | 67af5a4a6ed541b1b425de89fd05c2a74a265571 /vorlesungen/slides/dreieck/dichte.tex | |
parent | improved Einleitung (diff) | |
parent | Merge pull request #39 from NaoPross/master (diff) | |
download | SeminarSpezielleFunktionen-e08392d4bacb9a54c3ab755fa6445514749b608f.tar.gz SeminarSpezielleFunktionen-e08392d4bacb9a54c3ab755fa6445514749b608f.zip |
Merge branch 'master' of https://github.com/AndreasFMueller/SeminarSpezielleFunktionen
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/dreieck/dichte.tex | 67 |
1 files changed, 67 insertions, 0 deletions
diff --git a/vorlesungen/slides/dreieck/dichte.tex b/vorlesungen/slides/dreieck/dichte.tex new file mode 100644 index 0000000..168523a --- /dev/null +++ b/vorlesungen/slides/dreieck/dichte.tex @@ -0,0 +1,67 @@ +% +% dichte.tex -- Wahrscheinlichkeitsdichte +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Wahrscheinlichkeitsdichte} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.40\textwidth} +\begin{block}{Definition} +\[ +\varphi_{X_{k:n}}(x) += +\frac{d}{dx} F_{X_{k:n}}(x) +\] +\end{block} +\end{column} +\begin{column}{0.60\textwidth} +\uncover<4->{% +\begin{block}{Gleichverteilung} +\[ +{\color{darkgreen}F(x)}=\begin{cases} +0&x \le 0\\ +x&0\le x \le 1,\\ +1&x\ge 1 +\end{cases} +\quad +\uncover<5->{ +{\color{red}\varphi(x)} += +\begin{cases} +1&0\le x \le 1\\ +0&\text{sonst} +\end{cases}} +\] +\end{block}} +\end{column} +\end{columns} +\uncover<2->{% +\begin{block}{Ordnungsstatistik} +nach einiger Rechnung: +\begin{align*} +\varphi_{X_{k:n}}(x) +&= +{\color<3->{red}\varphi_X(x)}\,k\binom{n}{k}{\color<3->{darkgreen}F_X(x)}^{k-1} +(1-{\color<3->{darkgreen}F_X(x)})^{n-k} +\intertext{\uncover<4->{für Gleichverteilung}} +\uncover<6->{ +\varphi_{X_{k:n}}(x) +&= +\begin{cases} +\displaystyle +{\color<7->{blue}k\binom{n}{k}}{\color{darkgreen}x}^{k-1}(1-{\color{darkgreen}x})^{n-k} +&0\le x \le 1\\ +0&\text{sonst} +\end{cases} +\qquad\uncover<7->{\text{({\color{blue}Normierung})}} +} +\end{align*} +\end{block}} +\end{frame} +\egroup |