From 31b40de191bad98c212b65df7d7fc1a91f944036 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Wed, 21 Jan 2026 10:26:08 +0100
Subject: [PATCH] Add summary slide for theory 1

---
 src/2026-01-30/presentation.tex | 54 ++++++++++++++++++++++++++++++++-
 1 file changed, 53 insertions(+), 1 deletion(-)

diff --git a/src/2026-01-30/presentation.tex b/src/2026-01-30/presentation.tex
index d567ea6..52d98dc 100644
--- a/src/2026-01-30/presentation.tex
+++ b/src/2026-01-30/presentation.tex
@@ -116,6 +116,57 @@
 
 % TODO: Write
 
+\begin{frame}
+    \frametitle{Zusammenfassung}
+    
+    \vspace*{-15mm}
+
+    \begin{columns}[t]
+        \column{\kitthreecolumns}
+        \begin{greenblock}{Korrelationskoeffizient}
+            \vspace*{-8mm}
+            \begin{align*}
+                \rho_{XY} = \frac{\text{cov}(X,Y)}{\sqrt{V(X)V(Y)}}
+            \end{align*}
+        \end{greenblock}
+        \column{\kitthreecolumns}
+        \begin{greenblock}{Kovarianz}
+            \vspace*{-8mm}
+            \begin{align*}
+                \text{cov}(X,Y) = E(X,Y) - E(X)E(Y)
+            \end{align*}
+        \end{greenblock}
+    \end{columns}
+
+    \begin{columns}[t]
+        \column{\kitthreecolumns}
+        \begin{greenblock}{Erwartungswert}
+            \vspace*{-8mm}
+            \begin{align*}
+                E(X) &= \int_{-\infty}^{\infty} x f_X(x) dx \\
+                E(g(X)) &= \int_{-\infty}^{\infty} g(x) f_X(x) dx
+            \end{align*}
+            \begin{align*}
+                E(X + b) &= E(X) + b \\
+                E(X + Y) &= E(X) + E(Y) \\
+                E(aX) &= a E(X)
+            \end{align*}
+        \end{greenblock}
+        \column{\kitthreecolumns}
+        \begin{greenblock}{Varianz}
+            \vspace*{-8mm}
+            \begin{align*}
+                V(X) &= E\big( (X - E(X))^2 \big)
+            \end{align*}
+            \begin{align*}
+                V(X) &= E(X^2) - (E(X))^2 \\
+                V(aX) &= a^2 V(X) \\
+                V(X + b) &= V(X)
+            \end{align*}
+        \end{greenblock}
+    \end{columns}
+\end{frame}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Aufgabe}
 
@@ -336,7 +387,8 @@
             P(125 \le \tilde{S}_N \le 180)
         \end{align*}
     \end{minipage}
-    \pause\begin{minipage}[t]{0.3\textwidth}
+    \pause
+    \begin{minipage}[t]{0.3\textwidth}
         \centering
         \vspace*{-10mm}
         \begin{align*}