diff --git a/semester4/ps/ps-rb/main.pdf b/semester4/ps/ps-rb/main.pdf
index 35abd01..71850b8 100644
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diff --git a/semester4/ps/ps-rb/parts/02_variables.tex b/semester4/ps/ps-rb/parts/02_variables.tex
index 3199e9b..ada6493 100644
--- a/semester4/ps/ps-rb/parts/02_variables.tex
+++ b/semester4/ps/ps-rb/parts/02_variables.tex
@@ -245,9 +245,38 @@ $$
 \end{enumerate}
 \subtext{(2) wird \textit{Gedächtnislosigkeit} genannt.}
 
+\newpage
+
 \definition \textbf{Normalverteilung} $X \sim \mathcal{N}(m, \sigma^2)$
 $$
     f_X(x) = \frac{1}{ \sqrt{2\pi\sigma^2} } e^{ -\frac{(x-m)^2}{2\sigma^2} }
 $$
 
-\lemma \textbf{Eigenschaften von} $\mathcal{N}$
+\begin{center}
+    \includegraphics[width=0.5\linewidth]{res/normal-distribution.png}
+\end{center}
+
+\lemma \textbf{Summe von Normalverteilten ist normalverteilt}\\
+\smalltext{$X_1,\ldots,X_n$ unabh. s.d. $X_i \sim \mathcal{N}(m_i,\sigma_i^2)$}
+\begin{align*}
+    Z &= m_0 + \lambda_1X_1 + \ldots + \lambda_nX_n \\
+    Z &\sim \mathcal{N}\Biggl( \underbrace{m_0 + \sum_{i=1}^n \lambda_iX_i}_{m_Z}\quad,\quad \underbrace{\sum_{i=1}^n \lambda_i^2 \sigma_i^2}_{\sigma^2_Z} \Biggr)
+\end{align*}
+
+\definition \textbf{Standardnormalverteilung} 
+$$X \sim \mathcal{N}(0,1) \qquad \Phi(x) := \P[X \leq x]$$
+
+\lemma \textbf{Symmetrie} $\quad \Phi(-x) = 1-\Phi(x)$
+
+
+\lemma \textbf{Normalverteilung via } $\mathcal{N}(0,1)$\\
+\smalltext{$Z \sim \mathcal{N}(m, \sigma^2) \text{ arbiträr},\quad X \sim \mathcal{N}(0,1)$}
+$$
+    Z = m + \sigma\cdot X
+$$
+
+\lemma \textbf{Standardisierung}\\
+\smalltext{$Z \sim \mathcal{N}(m, \rho^2),\quad x\in\R$}
+$$
+    \P[x\leq Z] = \Phi\Biggl( \frac{x - m}{\rho} \Biggr)
+$$
\ No newline at end of file
diff --git a/semester4/ps/ps-rb/parts/03_expectation.tex b/semester4/ps/ps-rb/parts/03_expectation.tex
index 5f13b12..59eed22 100644
--- a/semester4/ps/ps-rb/parts/03_expectation.tex
+++ b/semester4/ps/ps-rb/parts/03_expectation.tex
@@ -128,6 +128,15 @@ $$
     \mathbb{V}[X] = \E[X^2]-\E[X]^2 
 $$
 
+{\footnotesize
+    \textbf{Beispiel:} Bestimme $\E\bigl[X^2\bigr]$, wobei $X \sim \text{Poisson}(\lambda)$, $\lambda > 0$. 
+    \begin{align*}
+        \V[X]               &= \E\bigl[X^2\bigr] - \E[X]^2      & (X \sim \text{Poisson}(\lambda))      \\
+        \lambda             &= \E\bigl[X^2\bigr] - \lambda^2                                            \\
+        \lambda + \lambda^2 &= \E\bigl[X^2\bigr]                                                        \\
+    \end{align*}
+}
+
 \lemma \textbf{Eigenschaften}
 \begin{align*}
     \text{(i)}      &\quad \V[X]        \geq 0         \\
diff --git a/semester4/ps/ps-rb/res/normal-distribution.png b/semester4/ps/ps-rb/res/normal-distribution.png
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