diff --git a/semester4/ps/ps-rb/main.pdf b/semester4/ps/ps-rb/main.pdf
index 71850b8..3de8312 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/parts/02_variables.tex b/semester4/ps/ps-rb/parts/02_variables.tex
index ada6493..e2cbadf 100644
--- a/semester4/ps/ps-rb/parts/02_variables.tex
+++ b/semester4/ps/ps-rb/parts/02_variables.tex
@@ -43,6 +43,18 @@ $$
     (iii)   & $\underset{a \to -\infty}{\lim} F_X(a) = 0 \quad\land\quad \underset{a \to \infty}{\lim}F_X(a)=1$
 \end{tabular}
 
+{\footnotesize
+    \textbf{Beispiel:} Zeige, dass $F$ eine Verteilungsfunktion ist:\\
+    $F(t) = \begin{cases}
+        0 & t \leq 0 \\
+        1-\exp(-\frac{t}{4}) & t > 0
+    \end{cases}$
+
+    (i) $F$ ist monoton wachsend, da $F'(t) = \frac{1}{4}\exp(-\frac{t}{4}) > 0 \forall t \in (-\infty, 0]$.\\
+    (ii) $F$ ist rechtsstetig, da $F$ eine Komp. stetiger Funktionen ist.\\
+    (iii) Es gilt $\underset{t\to-\infty}{\lim}F(t)=0$ und $\underset{t\to\infty}{\lim}F(t)=1$
+}
+
 \definition \textbf{Unabhängigkeit}\\
 \smalltext{$X_1,\cdots,X_n \text{ unabhängig } \iffdef§  \forall x_1,\cdots,x_n \in \R:$}
 $$
@@ -229,6 +241,10 @@ $$
     \end{cases}
 $$
 
+\lemma \textbf{Intervalle} $\quad \P\bigl[ X \in [c, c+l] \bigr] = \frac{l}{b-a}$\\
+\subtext{$X \sim \mathcal{U}([a,b])$}
+
+
 \definition \textbf{Exponentialverteilung} $T \sim \text{Exp}(\lambda)$
 $$
     f_T(x) = \begin{cases}
diff --git a/semester4/ps/ps-rb/parts/03_expectation.tex b/semester4/ps/ps-rb/parts/03_expectation.tex
index 59eed22..2861320 100644
--- a/semester4/ps/ps-rb/parts/03_expectation.tex
+++ b/semester4/ps/ps-rb/parts/03_expectation.tex
@@ -33,6 +33,8 @@ $$
         $\text{Poisson}(\lambda)$   & $\E[X] = \lambda$             & $\V[X] = \lambda$\\
         $\text{Bin}(n,p)$           & $\E[X] = n\cdot p$            & $\V[X] = np(1-p)$\\
         $\mathbb{I}_A$              & $\E[\mathbb{I}_A] = \P[A]$    \\
+        $\exp(\lambda)$             & $\E[X] = \frac{1}{\lambda}$   \\
+        $\mathcal{U}([a,b])$        & $\E[X] = \frac{a+b}{2}$ 
     \end{tabular}    
 \end{center}
 
@@ -166,11 +168,16 @@ $$
 
 \remark $\text{cov}(X,X) = \V[X]$
 
-\lemma $X,Y$ unabh. $\implies \text{cov}(X,Y)=0$\\
-\subtext{Nicht umgekehrt gültig}
-% Gegenbeispiel: Slides p.240
-
 \lemma \textbf{Eigenschaften von} $\text{cov}$
+\begin{align*}
+    \text{(i)}\quad         & \text{cov}(X,Y) \geq 0 \\
+    \text{(ii)}\quad        & \text{cov}(X,Y) = \text{cov}(Y,X) \\
+    \text{(iii)}\quad       & X,Y \text{ unabh. } \implies \text{cov}(X,Y) = 0 \\
+    \text{(iv)}\quad        & \V[X \pm Y] = \V[X] + \V[Y] \pm 2\text{cov}(X,Y) \\
+    \text{(v)}\quad         & \text{cov}\Biggl( \sum_{i=1}^{n}X_i,\sum_{j=1}^{n}Y_i \Biggr) = \sum_{i=1}^{n}\sum_{j=1}^{n}\text{cov}(X_i,Y_j) \\
+    \text{(vi)}\quad        & \text{cov}(aX+b, cY+d) = ac\cdot\text{cov}(X,Y) \\
+    \text{(vii)}\quad       & \text{cov}\Bigl(X, (eY+f) + (gZ+h)\Bigr) = e\text{cov}(X,Y) + g\text{cov}(X,Z)
+\end{align*}
 
 \definition \textbf{Kovarianzmatrix}
 $$