From f46373d0615f7697a74ad1ada41fe4acf8200f82 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Tue, 10 Feb 2026 09:23:42 +0100
Subject: [PATCH] Add exercises 1 and 2 for tutorial 7

---
 src/2026-02-13/presentation.tex | 228 ++++++++++++++++++++++++++++++++
 src/2026-02-13/res/boxplot.pdf  | Bin 0 -> 5951 bytes
 2 files changed, 228 insertions(+)
 create mode 100644 src/2026-02-13/presentation.tex
 create mode 100644 src/2026-02-13/res/boxplot.pdf

diff --git a/src/2026-02-13/presentation.tex b/src/2026-02-13/presentation.tex
new file mode 100644
index 0000000..4b2b6f2
--- /dev/null
+++ b/src/2026-02-13/presentation.tex
@@ -0,0 +1,228 @@
+\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{}
+
+%
+%
+% Document setup
+%
+%
+
+\usepackage{tikz}
+\usepackage{tikz-3dplot}
+\usetikzlibrary{spy, external, intersections, positioning}
+
+% \ifdefined\ishandout\else
+% \tikzexternalize
+% \fi
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+\usepgfplotslibrary{groupplots}
+
+\usepackage{enumerate}
+\usepackage{listings}
+\usepackage{subcaption}
+\usepackage{bbm}
+\usepackage{multirow}
+\usepackage{xcolor}
+\usepackage{amsmath}
+\usepackage{graphicx}
+\usepackage{calc}
+\usepackage{amssymb}
+
+\title{WT Tutorium 7}
+\author[Tsouchlos]{Andreas Tsouchlos}
+\date[]{13. Februar 2026}
+
+%
+%
+% Custom commands
+%
+%
+
+\input{lib/latex-common/common.tex}
+\pgfplotsset{colorscheme/rocket}
+
+\newcommand{\res}{src/2026-02-13/res}
+
+\newlength{\depthofsumsign}
+\setlength{\depthofsumsign}{\depthof{$\sum$}}
+\newlength{\totalheightofsumsign}
+\newcommand{\nsum}[1][1.4]{
+    \mathop{
+        \raisebox
+        {-#1\depthofsumsign+1\depthofsumsign}
+        {\scalebox
+            {#1}
+            {$\displaystyle\sum$}%
+        }
+    }
+}
+
+% \tikzstyle{every node}=[font=\small]
+% \captionsetup[sub]{font=small}
+
+\newlength{\hght}
+\newlength{\wdth}
+
+\newcommand{\canceltotikz}[3][.5ex]{
+    \setlength{\hght}{\heightof{$#3$}}
+    \setlength{\wdth}{\widthof{$#3$}}
+    \makebox[0pt][l]{
+        \tikz[baseline]{\draw[-latex](0,-#1)--(\wdth,\hght+#1)
+            node[shift={(2mm,2mm)}]{#2};
+        }
+    }#3
+}
+
+%
+%
+% Document body
+%
+%
+
+\begin{document}
+
+\begin{frame}[title white vertical, picture=images/IMG_7801-cut]
+    \titlepage
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Aufgabe 1}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Theorie Wiederholung}
+
+% TODO: Add slides
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Aufgabe}
+
+\begin{frame}
+    \frametitle{Aufgabe 1: Punktschätzer}
+
+    Die Anzahl der Studierenden, die zur Mittagszeit in der KIT-Mensa
+    essen gehen, sei näherungsweise Poissonverteilt mit unbekanntem
+    Parameter $\lambda > 0$, wobei $\lambda$ die mittlere Ankunftsrate an
+    Studierenden pro Minute ist.
+    \begin{gather*}
+        X_i \sim \text{Poisson}(\lambda),\hspace*{10mm} P(X_i = k
+        \vert \lambda) = \frac{\lambda^k}{k!}
+        e^{-\lambda},\hspace*{3mm} k\in \mathbb{N}_0
+    \end{gather*}
+    Aus N statistisch unabhängigen Messungen xi soll nun die mittlere
+    Ankunftsrate mithilfe eines
+    ML-Schätzers geschätzt werden.
+
+    \begin{enumerate}%
+        % tex-fmt: off
+    [a{)}]
+        % tex-fmt: on
+        \item Bestimmen Sie die Log-Likelihoodfunktion für $N$
+            Messwerte und damit den ML-Schätzer für die Ankunftsrate $\lambda$.
+        \item Zeigen Sie, dass der Schätzer erwartungstreu ist.
+        \item Ist der ML-Schätzer konsistent?
+        \item Ist der ML-Schätzer effizient?
+    \end{enumerate}
+
+\end{frame}
+% TODO: Add slides
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Aufgabe 2}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Theorie Wiederholung}
+
+% TODO: Add slides
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Aufgabe}
+
+\begin{frame}
+    \frametitle{Aufgabe 2: Deskriptive Statistik}
+
+    \vspace*{-15mm}
+
+    \begin{enumerate}%
+        % tex-fmt: off
+    [a{)}]
+        % tex-fmt: on
+        \item Nennen Sie zwei Bedingungen, die erfüllt sein müssen,
+            damit eine Stichprobe als einfache
+            Stichprobe gilt. Wie muss eine Stichprobe vorverarbeitet
+            werden, um daraus den Median
+            oder Quantile bestimmen zu können?
+            % TODO: Insert plot
+        \item Lesen Sie aus dem Boxplot folgende Werte ab: den
+            Median, die untere Quartilsgrenze, die
+            größte normale Beobachtung.
+    \end{enumerate}
+
+    \vspace*{5mm}
+    \begin{figure}[H]
+        \centering
+        \includegraphics[scale=1.4]{res/boxplot.pdf}
+    \end{figure}
+    \vspace*{5mm}
+
+    Die Zufallsvariable $Z \in \mathbb{N}$ beschreibt die
+    Studiendauer am KIT bis zum Abschluss der Promotion. Eine
+    einfache Zufallsstichprobe mit $n = 6$ Studierenden ergab die
+    folgenden Studiendauern:
+    \begin{gather*}
+        z_1 =
+        \begin{pmatrix}
+            28 & 22 & 25 & 26 & 25 & 24
+        \end{pmatrix}
+    \end{gather*}
+
+    Durch fehlerhaftes Eintragen wurde für zwei weitere Studierende
+    die Studiendauer $0$ und $129$ vermerkt. Die erweiterte Stichprobe lautet:
+    \vspace*{-5mm}
+    \begin{gather*}
+        z_1 =
+        \begin{pmatrix}
+            28 & 22 & 25 & 26 & 25 & 24 & 0 & 129
+        \end{pmatrix}
+    \end{gather*}
+
+    \vspace*{5mm}
+
+    \begin{enumerate}%
+        % tex-fmt: off
+    [a{)}]
+        % tex-fmt: on
+            \setcounter{enumi}{2}
+        \item Berechnen Sie für beide Stichproben die empirische
+            Varianz und den Quartilsabstand. Erklären Sie anhand der
+            Ergebnisse einen Vorteil des Quartilsabstands gegenüber
+            der Varianz als Maß für die Streuung.
+    \end{enumerate}
+
+\end{frame}
+% TODO: Add slides
+
+\end{document}
+
diff --git a/src/2026-02-13/res/boxplot.pdf b/src/2026-02-13/res/boxplot.pdf
new file mode 100644
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