Add tutorial 1 exercise slides
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3
Makefile
3
Makefile
@ -3,6 +3,9 @@ all:
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TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk src/template/presentation.tex
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mv build/presentation.pdf build/presentation_template.pdf
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TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk src/2025-11-07/presentation.tex
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mv build/presentation.pdf build/presentation_2025-11-07.pdf
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clean:
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rm -rf build
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0
src/2025-11-07/presentation.bib
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src/2025-11-07/presentation.bib
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src/2025-11-07/presentation.tex
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src/2025-11-07/presentation.tex
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\documentclass[de]{CELbeamer}
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%
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%
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% CEL Template
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%
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%
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\newcommand{\templates}{preambles}
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\input{\templates/packages.tex}
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\input{\templates/macros.tex}
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\grouplogo{CEL_logo.pdf}
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\groupname{Communication Engineering Lab (CEL)}
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\groupnamewidth{80mm}
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\fundinglogos{}
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%
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%
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% Custom commands
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%
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%
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\input{lib/latex-common/common.tex}
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\pgfplotsset{colorscheme/rocket}
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%TODO: Fix path
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\newcommand{\res}{src/template/res}
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% \tikzstyle{every node}=[font=\small]
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% \captionsetup[sub]{font=small}
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%
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%
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% Document setup
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%
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%
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\usepackage{tikz}
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\usepackage{tikz-3dplot}
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\usetikzlibrary{spy, external, intersections}
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%\tikzexternalize[prefix=build/]
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\usepackage{pgfplots}
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\pgfplotsset{compat=newest}
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\usepgfplotslibrary{fillbetween}
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\usepackage{enumerate}
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\usepackage{listings}
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\usepackage{subcaption}
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\usepackage{bbm}
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\usepackage{multirow}
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\usepackage{xcolor}
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\title{WT Tutorium 1}
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\author[Tsouchlos]{Andreas Tsouchlos}
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\date[]{\today}
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%
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%
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% Document body
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%
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%
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\begin{document}
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\begin{frame}[title white vertical, picture=images/IMG_7801-cut]
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\titlepage
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Aufgabe 1}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Theorie}
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% TODO: Replace slide content with relevant stuff
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\begin{frame}
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\frametitle{Relevante Theorie I}
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\begin{columns}
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\column{\kitthreecolumns}
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\begin{greenblock}{Zufallsvariablen (ZV)}%
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\vspace*{-6mm}
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\begin{gather*}
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f_X(x) := \frac{d}{dx} F_X(x) \\
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P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
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E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
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\end{gather*}
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\end{greenblock}
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\column{\kitthreecolumns}
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\begin{greenblock}{Important Equations}%
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\vspace*{-6mm}
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\begin{gather*}
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f_X(x) := \frac{d}{dx} F_X(x) \\
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P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
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E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
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\end{gather*}
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\end{greenblock}
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\end{columns}
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\begin{greenblock}{Normalverteilung}
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\begin{columns}
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\column{\kitthreecolumns}
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\begin{gather*}
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\text{Normalverteilung:} \hspace{8mm}
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f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
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e^{-\frac{(x - \mu)^2}{2\sigma^2}}
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\end{gather*}
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\column{\kitthreecolumns}
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\begin{figure}
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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domain=-4:4,
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samples=100,
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width=11cm,
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height=6cm,
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ticks=none,
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xlabel={$x$},
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ylabel={$f_X(x)$}
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]
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\addplot+[mark=none, line width=1pt] {exp(-x^2)};
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\end{axis}
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\end{tikzpicture}
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\end{figure}
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\end{columns}
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\end{greenblock}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Aufgabe}
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% TODO: Replace slide content with relevant stuff
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\begin{frame}
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\frametitle{Aufgabe 1: Ergebnisraum \& Hypergeometrische\\ Verteilung}
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Bei einem Kartenspiel erhält ein Spieler 5 Karten aus einem Deck
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von 52 Karten (bestehend aus
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13 Arten mit je 4 Farben). Wie groß ist die Wahrscheinlichkeit,
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dass der Spieler
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% tex-fmt: off
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\begin{enumerate}[a{)}]
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\item mindestens ein Ass hat?
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\item genau ein Ass hat?
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\item mindestens zwei Karten der gleichen Art (“Paar”) hat?
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\end{enumerate}
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% tex-fmt: on
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Aufgabe 2}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Theorie}
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% TODO: Replace slide content with relevant stuff
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\begin{frame}
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\frametitle{Relevante Theorie II}
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\begin{gather*}
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f_X(x) := \frac{d}{dx} F_X(x) \\
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P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
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E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
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\end{gather*}
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\begin{figure}
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\centering
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{gather*}
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\text{Normalverteilung:} \hspace{8mm}
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f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
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e^{-\frac{(x - \mu)^2}{2\sigma^2}}
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\end{gather*}
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\end{subfigure}%
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\begin{subfigure}[c]{0.4\textwidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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domain=-4:4,
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samples=100,
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width=\textwidth,
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height=0.5\textwidth,
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ticks=none,
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xlabel={$x$},
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ylabel={$f_X(x)$}
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]
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\addplot+[mark=none, line width=1pt] {exp(-x^2)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\end{figure}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Aufgabe}
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% TODO: Replace slide content with relevant stuff
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\begin{frame}
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\frametitle{Aufgabe 2}
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Aufgabe 2: Variationen \& Permutationen
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Ein Burgerrestaurant bietet verschiedene Burger mit den Zutaten Salat
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(S), Käse (K), Tomate (T)
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und Patty (P) an. Diese werden zufällig für die Zubereitung eines
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Burgers ausgewählt.
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% tex-fmt: off
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\begin{enumerate}[a{)}]
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\item Die Ergebnismenge sei $\Omega = \{S, K, T, P\}$. Wie lautet die
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Potenzmenge $P(\Omega)$?
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\item Für einen normalen Burger werden 3 der 4 möglichen Zutaten
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ausgewählt und in einer
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bestimmten Reihenfolge auf das Burgerbrötchen gelegt. Wie viele
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verschiedene normale
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Burger gibt es?
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\item Ein Burger ``Spezial'' besteht ebenfalls aus 3 Zutaten. Jedoch
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können Tomate und Salat
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doppelt vorkommen. Wie viele verschiedene Burger „Spezial“ gibt es?
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\item Der Burger „Jumbo“ enthält die folgende Menge an Zutaten: $\{S, S,
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T, T, K, K, K, P, P, P\}$
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die alle verwendet werden. Wie viele mögliche Belegungen des Burgers
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``Jumbo'' gibt es?
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\end{enumerate}
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% tex-fmt: on
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Zusammenfassung}
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% TODO: Replace slide content with relevant stuff
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\begin{frame}
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\frametitle{Zusammenfassung}
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\begin{gather*}
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f_X(x) := \frac{d}{dx} F_X(x) \\
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P(X \le x) = F_X(x) = \int_{-\infty}^{x} f_X(t) dt \\
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E(X) = \int_{-\infty}^{\infty} x\cdot f_X(x) dx
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\end{gather*}
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\begin{figure}
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\centering
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{gather*}
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\text{Normalverteilung:} \hspace{8mm}
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f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}}
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e^{-\frac{(x - \mu)^2}{2\sigma^2}}
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\end{gather*}
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\end{subfigure}%
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\begin{subfigure}[c]{0.4\textwidth}
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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domain=-4:4,
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samples=100,
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width=\textwidth,
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height=0.5\textwidth,
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ticks=none,
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xlabel={$x$},
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ylabel={$f_X(x)$}
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]
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\addplot+[mark=none, line width=1pt] {exp(-x^2)};
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\end{figure}
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\end{frame}
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\end{document}
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