diff --git a/semester4/ps/ps-rb/main.pdf b/semester4/ps/ps-rb/main.pdf
index 7d0d5cc..359fd78 100644
Binary files a/semester4/ps/ps-rb/main.pdf and b/semester4/ps/ps-rb/main.pdf differ
diff --git a/semester4/ps/ps-rb/main.tex b/semester4/ps/ps-rb/main.tex
index dcf6e8d..8152b1b 100644
--- a/semester4/ps/ps-rb/main.tex
+++ b/semester4/ps/ps-rb/main.tex
@@ -8,7 +8,10 @@
 \date{HS 2026}
 
 \begin{document}
-\subtext{Basiert auf dem Skript von V. Tassion, Slides von E.W. Farkas (FS26)}
+\subtext{
+    Basiert auf dem Skript von V. Tassion, Slides von E.W. Farkas (FS26)
+    Die letzten 2 Seiten (Tabellen) auf einer Seite drucken. (10S. limit)
+}
 \input{parts/00_prereq.tex}
 
 \newpage
@@ -24,7 +27,7 @@
 \input{parts/04_joint-distributions.tex}
 
 \newpage
-\section{Erwartungswert}
+\section{Charakterisierung}
 \input{parts/03_expectation.tex}
 
 \newpage
diff --git a/semester4/ps/ps-rb/parts/00_prereq.tex b/semester4/ps/ps-rb/parts/00_prereq.tex
index 7d04a67..b5fb6c6 100644
--- a/semester4/ps/ps-rb/parts/00_prereq.tex
+++ b/semester4/ps/ps-rb/parts/00_prereq.tex
@@ -11,4 +11,11 @@ $$
     \binom{n}{k} := \frac{n!}{k!\cdot(n-k)!}
 $$
 
-% Integrationsmethoden, Integraltabelle
\ No newline at end of file
+\method \textbf{Partielle Integration}\\
+\subtext{$a<b,\quad f,g:[a,b]\rightarrow\R$ stetig diff.-bar}
+$$\int f(x)\cdot g'(x)\ dx = f(x)\cdot g(x) - \int f'(x)\cdot g(x)\ dx$$
+$$\int_a^bf(x)g'(x)\ dx = f(b)g(b) - f(a)g(a) -\int_a^b f'(x)g(x)$$
+
+\method \textbf{Substitution}\\
+\subtext{$a<b,\quad \phi:[a,b]\rightarrow\R$ stetig diff.-bar,\\ $I \subset \R,\quad \phi([a,b]) \subset I,\quad f: I\rightarrow\R$ stetig}
+$$\int_{\phi(a)}^{\phi(b)}f(x)\ dx = \int^b_af(\phi(t))\cdot\phi'(t)\ dt$$
diff --git a/semester4/ps/ps-rb/parts/03_expectation.tex b/semester4/ps/ps-rb/parts/03_expectation.tex
index bd85258..699df28 100644
--- a/semester4/ps/ps-rb/parts/03_expectation.tex
+++ b/semester4/ps/ps-rb/parts/03_expectation.tex
@@ -1,6 +1,6 @@
-\subsection{Allgemeiner Erwartungswert}
+\subsection{Erwartungswert}
 
-\definition \textbf{Erwartungswert} (nicht-negativ)
+\definition \textbf{Allg. Erwartungswert} (nicht-negativ)
 $$
     \E[X] = \int_{0}^{\infty} \biggl( 1-F_X(x) \biggr)\ dx
 $$
@@ -101,6 +101,15 @@ $$
     \V\Biggl[ \sum_{k=1}^{n}X_k \Biggr] = \sum_{k=1}^{n}\V[X_k]
 $$
 
+{\scriptsize
+    \textbf{Beispiel}: $\E[X^2]$ allgemein.
+    \begin{align*}
+        \E[X^2] &= \E[\phi(X)] \text{ s.d. } \phi(x) = x^2 \\
+                &\implies \E[X^2] = \int_{-\infty}^{+\infty}\phi(x)f_X(x)\ dx = \boxed{\int_{-\infty}^{+\infty} x^2 \cdot f_X(x)\ dx}
+    \end{align*}
+
+}
+
 \newpage
 \subsection{Kovarianz}
 
@@ -139,3 +148,15 @@ $$
     \end{bmatrix}
     $$
 }
+
+{\scriptsize
+    \textbf{Beispiel}: $\E\Bigl[\text{max}(X_1,\ldots,X_n)\Bigr]$ s.d. $X_1,\ldots,X_n \overset{\text{i.i.d.}}{\sim} \mathcal{X}$
+    \begin{align*}
+        F_{\max(X_1,\ldots,X_n)}(x)             &= \P[X_1\leq x,\ldots,X_n\leq x]           \\
+                                                &= \P[X_1\leq x] \cdots \P[X_n\leq x]       \\
+                                                &= (\P[X \leq x])^n = F_X(x)^n              \\
+        \implies f_{\max(X_1,\ldots,X_n)}(x)    &= \partial_x (F_X(x))^n                    \\
+        \implies \E[\max(X_1,\ldots,X_n)]       &= \boxed{\int_{-\infty}^{+\infty} x \cdot \partial_x \Bigl(F_X(x)\Bigr)^n}
+    \end{align*}
+
+}
diff --git a/semester4/ps/ps-rb/parts/04_joint-distributions.tex b/semester4/ps/ps-rb/parts/04_joint-distributions.tex
index 3ce2bbd..482e2b6 100644
--- a/semester4/ps/ps-rb/parts/04_joint-distributions.tex
+++ b/semester4/ps/ps-rb/parts/04_joint-distributions.tex
@@ -14,9 +14,9 @@ $$
 \theorem \textbf{Randverteilung}\\
 \smalltext{Die einzelnen Verteilungen $p_X$ lassen sich extrahieren:}\\
 \subtext{$\forall z \in W_i$:}
-$$
- \P[X_i = z] = \underset{x_1,\ldots,x_{i-1},z,x_{i+1},\ldots,x_n}{\sum} p\Bigl( x_1,\ldots,x_{i-1},z,x_{i+1},\ldots,x_n \Bigr)
-$$
+\begin{align*}
+ \P[X_i = z] = \underset{x_1,\ldots,z,\ldots,x_n}{\sum} p\Bigl( x_1,\ldots,x_{i-1},z,x_{i+1},\ldots,x_n \Bigr)
+\end{align*}
 \subtext{$X_1,\ldots,X_n$ diskret,$\quad$ gem. Vert. $p = \Bigl( p(x_1,\dots,x_n) \Bigr)_{x_1 \in W_1,\ldots,x_n \in W_n}$}
 
 {\footnotesize
@@ -26,11 +26,20 @@ $$
 
 \definition \textbf{Gemeinsame Stetige Verteilung}\\
 \smalltext{$X_1,\ldots,X_n: \Omega\to\R,\quad f:\R^n\to\R_+,\quad a_1,\ldots a_n \in \R$}
-$$
-    \P\Bigl[ X_1\leq a_1,\ldots,X_n\leq a_n \Bigr] = \int_{-\infty}^{a_1}\cdots\int_{-\infty}^{a_n} f(x_1,\ldots,x_n)\ dx_n\ldots dx_1
-$$
+\begin{align*}
+        &\P\Bigl[ X_1\leq a_1,\ldots,X_n\leq a_n \Bigr] \\
+        &= \int_{-\infty}^{a_1}\cdots\int_{-\infty}^{a_n} f(x_1,\ldots,x_n)\ dx_n\ldots dx_1    
+\end{align*}
+
 \subtext{$f$ heisst \textit{gemeinsame Dichte} von $(X_1,\ldots,X_n)$}
 
+{\footnotesize
+    \remark Seien $X_1,\ldots,X_n \overset{\text{i.i.d.}}{\sim} \mathcal{X}$:
+    \begin{align*}
+        &\P\Bigl[ X_1 \leq x,\ldots, X_n \leq x \Bigr] = \prod_{i=1}^n \P[X_i \leq n] = \Bigl( \P[X \leq n] \Bigr)^n
+    \end{align*}
+}
+
 \newpage
 
 \theorem $\displaystyle\int_{-\infty}^\infty\cdots\int_{-\infty}^\infty f(x_1,\ldots,x_n)\ dx_n\ dx_1 = 1$\\
@@ -59,10 +68,11 @@ $$
 
 % Bedingte Dichten fehlen noch, siehe HW5, F3
 
-\theorem \textbf{Erwartungswert}\\
-$$
-    \E\Bigl[ \phi(X_1,\ldots,X_n) \Bigr] = \int_{-\infty}^\infty\cdots\int_{-\infty}^\infty\phi(x_1,\ldots,x_n)\cdot f(x_1\cdots x_n)\ dx_n\ldots dx_1
-$$
+\theorem \textbf{Erwartungswert}
+\begin{align*}
+    &\E\Bigl[ \phi(X_1,\ldots,X_n) \Bigr] \\
+    &= \int_{-\infty}^\infty\cdots\int_{-\infty}^\infty\phi(x_1,\ldots,x_n)\cdot f(x_1\cdots x_n)\ dx_n\ldots dx_1    
+\end{align*}
 
 % Randverteilungen
 
diff --git a/semester4/ps/ps-rb/parts/06_limits.tex b/semester4/ps/ps-rb/parts/06_limits.tex
index 5016cb7..5d3dfb6 100644
--- a/semester4/ps/ps-rb/parts/06_limits.tex
+++ b/semester4/ps/ps-rb/parts/06_limits.tex
@@ -54,4 +54,8 @@ $$
 $$
 \subtext{Im Skript auch $Z_n$}
 
-% Slides: Chernoff bounds & mehr ZGS (nicht im Skript)
\ No newline at end of file
+% Slides: Chernoff bounds & mehr ZGS (nicht im Skript)
+
+\newpage
+
+div % s.d. Statistik auf einer Seite bleibt
\ No newline at end of file
diff --git a/semester4/ps/ps-rb/parts/07_stats.tex b/semester4/ps/ps-rb/parts/07_stats.tex
index 8148aab..2a61735 100644
--- a/semester4/ps/ps-rb/parts/07_stats.tex
+++ b/semester4/ps/ps-rb/parts/07_stats.tex
@@ -396,10 +396,4 @@ $$
 \begin{align*}
     &   I = [A,B] \text{ s.d. } \P\Bigl[ \vartheta \in [A,B] \Bigr] = \P[A\leq\vartheta\leq B] \geq 1-\alpha \\
     &   A = a(X_1,\ldots,X_n) \qquad B = b(X_1,\ldots,X_n)
-\end{align*}
-
-\newpage
-
-div
-
-\newpage
\ No newline at end of file
+\end{align*}
\ No newline at end of file
diff --git a/semester6/iml/main.pdf b/semester6/iml/main.pdf
index 99c13c3..c2415a8 100644
Binary files a/semester6/iml/main.pdf and b/semester6/iml/main.pdf differ
diff --git a/semester6/iml/parts/04_networks.tex b/semester6/iml/parts/04_networks.tex
index 5e77aac..435a090 100644
--- a/semester6/iml/parts/04_networks.tex
+++ b/semester6/iml/parts/04_networks.tex
@@ -23,7 +23,7 @@ $$
 We set $\phi_i(x;\theta_i) = \psi(\theta_i^\top x)$, $\psi$ is the activation function.\\
 \subtext{$\theta_i \in \R^d,\quad\psi:\R\to\R$}
 
-{\scriptsize
+{\footnotesize
     \notation More concisely, $\phi(x;\Theta) = \psi(\Theta x)$
 }
 
@@ -38,6 +38,12 @@ We set $\phi_i(x;\theta_i) = \psi(\theta_i^\top x)$, $\psi$ is the activation fu
     \end{tabular}
 \end{center}
 
+{\footnotesize
+    \remark \textbf{Derivative of Sigmoid} $\quad \sigma(x)' = \sigma(x)\cdot (1-\sigma(x))$
+}
+
+\newpage
+
 \definition \textbf{Artificial Neural Network}\\
 \subtext{The output functions of the above problem take the form:}
 $$
@@ -47,7 +53,6 @@ $$
     \remark Also called Multi-Layer Perceptron (MLP)
 }
 
-\newpage
 \textbf{What is happening here?}\\
 \smalltext{Explaining the calculation steps for such an $f$ naturally leads to the common pictorial depiction of neural networks.}
 \begin{align*}