Add slide explaining prob. theory vs statistics

src/2026-02-13/presentation.tex

@@ -114,7 +114,172 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Theorie Wiederholung}
 
-% TODO: Add slides
+\begin{frame}
+    \frametitle{Wahrscheinlichkeitstheorie und Statistik}
+
+    \vspace*{-5mm}
+
+    \begin{itemize}
+        \item Einfache Stichprobe
+            \begin{gather*}
+                X_1, \ldots, X_N \hspace{2mm}\overbrace{\text{unabhäng und haben
+                dieselbe Verteilung}}^{\text{``iid.''}}
+                \hspace*{5mm} \rightarrow\hspace*{5mm}
+                \bm{X} :=
+                \begin{pmatrix}
+                    X_1 \\
+                    \vdots \\
+                    X_N
+                \end{pmatrix}
+            \end{gather*}
+    \end{itemize}
+
+    \pause
+    \begin{figure}[H]
+        \centering
+
+        \begin{subfigure}{0.5\textwidth}
+            \centering
+
+            \begin{itemize}
+                \item Wahrscheinlichkeitstheorie
+            \end{itemize}
+            \vspace*{2mm}
+            \begin{tikzpicture}
+                \node[
+                    rectangle,
+                    minimum width=7cm, minimum height=4cm,
+                    line width=1pt,
+                    draw=kit-blue, fill=kit-blue!20,
+                ] (model) {
+                    $\bm{X} =
+                    \begin{pmatrix}
+                        X_1 \\
+                        \vdots \\
+                        X_N
+                    \end{pmatrix}\sim P_{\bm{X}}$
+                };
+
+                \node[right=of model] (x) {
+                    $\bm{x} =
+                    \begin{pmatrix}
+                        x_1 \\
+                        \vdots \\
+                        x_N
+                    \end{pmatrix}$
+                };
+
+                \draw[-{Latex}, line width=1pt] (model) -- (x);
+                \node[above=22mm of model.center] {Modell};
+                \node[above=20.8mm of x.center] {Beobachtung};
+            \end{tikzpicture}%
+            \vspace*{15mm}
+        \end{subfigure}%
+        \only<2>{\hspace*{16cm}}%
+        \only<3->{\vspace*{-12.6mm}}%
+        \begin{subfigure}{0.5\textwidth}
+            \centering
+
+            \only<3>{
+                \begin{itemize}
+                    \item Statistik
+                \end{itemize}
+                \begin{tikzpicture}
+                    \node[
+                        rectangle,
+                        minimum width=7.5cm, minimum height=4.5cm,
+                        line width=1pt,
+                        draw=kit-orange, fill=kit-orange!20,
+                    ] (real) {};
+
+                    \node[right=of real] (x) {
+                        $\bm{x} =
+                        \begin{pmatrix}
+                            x_1 \\
+                            \vdots \\
+                            x_N
+                        \end{pmatrix}$
+                    };
+
+                    \draw[-{Latex}, line width=1pt] (real) -- (x);
+                    \node[above=23mm of real.center] {``Echte Welt''};
+                    \node[above=21.8mm of x.center] {Beobachtung};
+
+                    \node[below=25.5mm of real.center]
+                    {\phantom{Modellierung}};
+                \end{tikzpicture}
+            }%
+            \only<4->{
+                \begin{itemize}
+                    \item Statistik
+                \end{itemize}
+                \begin{tikzpicture}
+                    \node[
+                        rectangle,
+                        minimum width=7.5cm, minimum height=4.5cm,
+                        line width=1pt,
+                        draw=kit-orange, fill=kit-orange!20,
+                    ] (real) {};
+
+                    \node[right=of real] (x) {
+                        $\bm{x} =
+                        \begin{pmatrix}
+                            x_1 \\
+                            \vdots \\
+                            x_N
+                        \end{pmatrix}$
+                    };
+
+                    \draw[-{Latex}, line width=1pt] (real) -- (x);
+                    \node[above=23mm of real.center] {``Echte Welt''};
+                    \node[above=21.8mm of x.center] {Beobachtung};
+
+                    \node[
+                        rectangle,
+                        minimum width=6.5cm, minimum height=3.5cm,
+                        line width=1pt,
+                        draw=kit-blue, fill=kit-blue!20,
+                        densely dashed,
+                    ] (model) at (real) {
+                        $\bm{X} =
+                        \begin{pmatrix}
+                            X_1 \\
+                            \vdots \\
+                            X_N
+                        \end{pmatrix}\sim P_{\bm{X}}$
+                    };
+
+                    \draw[
+                        line width=1pt, densely dashed,
+                    ] (x.south)
+                    edge[-{Latex}, bend left]
+                    node[below] {Modellierung}
+                    (model.south);
+                \end{tikzpicture}
+            }
+            \vspace*{1mm}
+        \end{subfigure}
+        \only<3->{
+            \vspace*{12.5mm}
+        }
+    \end{figure}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Schätzer I}
+
+    \begin{itemize}
+        \item asdf
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Schätzer II}
+
+    \begin{itemize}
+        \item asdf
+    \end{itemize}
+\end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Aufgabe}
@@ -139,13 +304,14 @@
     [a{)}]
         % tex-fmt: on
         \item Bestimmen Sie die Log-Likelihoodfunktion für $N$
-            Messwerte und damit den ML-Schätzer für die Ankunftsrate $\lambda$.
+            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
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -198,7 +364,8 @@
     \end{gather*}
 
     Durch fehlerhaftes Eintragen wurde für zwei weitere Studierende
-    die Studiendauer $0$ und $129$ vermerkt. Die erweiterte Stichprobe lautet:
+    die Studiendauer $0$ und $129$ vermerkt. Die erweiterte
+    Stichprobe lautet:
     \vspace*{-5mm}
     \begin{gather*}
         z_1 =