From 7e67ee3792b80bc136c844b4024a82a365ee0966 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Sun, 21 Dec 2025 16:24:43 +0100
Subject: [PATCH] Add slides with exercises for tutorial 5

---
 src/2026-01-16/presentation.tex | 138 ++++++++++++++++++++++++++++++++
 1 file changed, 138 insertions(+)
 create mode 100644 src/2026-01-16/presentation.tex

diff --git a/src/2026-01-16/presentation.tex b/src/2026-01-16/presentation.tex
new file mode 100644
index 0000000..ec338ed
--- /dev/null
+++ b/src/2026-01-16/presentation.tex
@@ -0,0 +1,138 @@
+\ifdefined\ishandout
+\documentclass[de, handout]{CELbeamer}
+\else
+\documentclass[de]{CELbeamer}
+\fi
+
+%
+%
+% CEL Template
+%
+%
+
+\newcommand{\templates}{preambles}
+\input{\templates/packages.tex}
+\input{\templates/macros.tex}
+
+\grouplogo{CEL_logo.pdf}
+
+\groupname{Communication Engineering Lab (CEL)}
+\groupnamewidth{80mm}
+
+\fundinglogos{}
+
+%
+%
+% Custom commands
+%
+%
+
+\input{lib/latex-common/common.tex}
+\pgfplotsset{colorscheme/rocket}
+
+\newcommand{\res}{src/2026-01-16/res}
+
+% \tikzstyle{every node}=[font=\small]
+% \captionsetup[sub]{font=small}
+
+%
+%
+% Document setup
+%
+%
+
+\usepackage{tikz}
+\usepackage{tikz-3dplot}
+\usetikzlibrary{spy, external, intersections, positioning}
+%\tikzexternalize[prefix=build/]
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+
+\usepackage{enumerate}
+\usepackage{listings}
+\usepackage{subcaption}
+\usepackage{bbm}
+\usepackage{multirow}
+
+\usepackage{xcolor}
+
+\title{WT Tutorium 5}
+\author[Tsouchlos]{Andreas Tsouchlos}
+\date[]{16. Januar 2026}
+
+%
+%
+% Document body
+%
+%
+
+\begin{document}
+
+\begin{frame}[title white vertical, picture=images/IMG_7801-cut]
+    \titlepage
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Aufgabe 1}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Theorie Wiederholung}
+
+% TODO:
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Aufgabe}
+
+\begin{frame}
+    \frametitle{Aufgabe 1:\\Faltungssatz \& Charakteristische Funktion}
+
+    Es seien zwei unabhängige poissonverteilte Zufallsvariablen $X$ und
+    $Y$ mit den Parametern $\lambda_1$
+    bzw. $\lambda_2$ gegeben.
+
+    % tex-fmt: off
+    \begin{enumerate}[a{)}]
+        \item Zeigen Sie, dass die Summe $Z = X + Y$ ebenfalls
+            Poisson-verteilt ist mit dem Parameter $\lambda = \lambda_1 +
+            \lambda_2$. Nutzen Sie dazu den Faltungssatz für die Addition
+            zweier Zufallsvariablen.
+        \item Erbringen Sie denselben Nachweis mithilfe der
+            charakteristischen Funktion.
+    \end{enumerate}
+    % tex-fmt: on
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Aufgabe 2}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Theorie Wiederholung}
+
+% TODO:
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Aufgabe}
+
+\begin{frame}
+    \frametitle{Aufgabe 2: Transformationssatz für 2D-Dichten}
+
+    Die Zufallsvariable $(X; Y)^T$ habe die gemeinsame
+    Wahrscheinlichkeitsdichte $f (x, y) = x + y$ für
+    $x, y \in (0; 1]$ und null sonst.
+
+    % tex-fmt: off
+    \begin{enumerate}[a{)}]
+        \item Berechnen Sie die Dichte von $(Z = X \cdot Y)$ mithilfe des
+            Transformationssatzes.
+        \item Verwenden Sie einen alternativen Ansatz zur Berechnung der
+            Dichte. Hinweis: Beginnen Sie mit $P (Z \le z) = \ldots$
+        \item Berechnen Sie den Korrelationskoeffizienten $\rho_{XY}$ .
+    \end{enumerate}
+    % tex-fmt: on
+
+\end{frame}
+
+\end{document}
+