diff --git a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex
index 9b68fd5..e6e937a 100644
--- a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex
+++ b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex
@@ -5,6 +5,7 @@
 
 \subsubsection{Beispiele}
 % TODO: Consider if need derivation of them here and prev section as well
+% TODO: Also add the ones proven in exercises
 \shortlemma[Int über gauss. Glockenk.] $\int_{-\8}^{\8} e^{\frac{-x^2}{2\sigma^2}} \dx x = \sqrt{2 \pi \sigma^2}$
 \begin{itemize}
     \item $\cX \sim \cU([a, b])$, $a < b$: $\E[\cX] = \frac{a + b}{2}$
diff --git a/semester4/ps/ps-jh/parts/03_expected-value/03_properties.tex b/semester4/ps/ps-jh/parts/03_expected-value/03_properties.tex
new file mode 100644
index 0000000..6c84ba8
--- /dev/null
+++ b/semester4/ps/ps-jh/parts/03_expected-value/03_properties.tex
@@ -0,0 +1,20 @@
+\subsection{Eigenschaften des Erwartungswerts}
+\shorttheorem[Linearität] Falls $\E[\cX]$ und $\E[\cY]$ wohldefiniert:\\
+$\E[\lambda \cX] = \lambda \E[\cX]$ und $\E[\cX + \cY] = \E[\cX] + \E[\cY]$
+
+\shortremark Z.V $\cX_k$ und $\lambda_k$: $\E\left[ \sum_{k = 1}^{n} \lambda_k \cX_k \right] = \sum_{k = 1}^{n} \lambda_k \E[\cX_k]$
+
+\shorttheorem[Monotonie] Sei $\cX \leq \cY$ mit $\E$ wohldef.: $\E[\cX] \leq \E[\cY]$
+
+\shorttheorem $\cX, \cY$ unabh., dann $\E[\cX \cY] = \E[\cX] \E[\cY]$
+
+\shorttheorem $\cX_k$ alle unabhängig mit $\E[\cX_k]$ endlich. Dann gilt\\
+$\E\left[ \prod_{k = 1}^n \cX_k \right] = \prod_{k = 1}^n \E[\cX_k]$
+
+\shorttheorem $f : \R \rightarrow \R_+$ mit $\int_{-\8}^{\8} f(x) \dx x = 1$. Dann ist äquivalent:
+\bi{(1)} $\cX$ stetig mit Dichte $f$ und \bi{(2)} für jede stückweise stetige Abb. $\varphi : \R \rightarrow \R$ gilt $\E[\varphi(\cX)] = \int_{-\8}^{\8} \varphi(x) f(x) \dx x$
+
+\shorttheorem äquivalent: \bi{1} $\cX, \cY$ unabhängig, für alle $\varphi, \psi : \R \rightarrow \R$: $\E[\varphi(\cX) \psi(\cX)] = \E[\varphi(\cX)] \E[\psi]$
+
+\shorttheorem äquivalent: \bi{(1)} $\cX_i$ unabhängig,\\
+\bi{(2)} $\forall \varphi_i$: $\E[\varphi_1(\cX_1) \cdots \varphi_n(\cX_n)] = \E[\varphi_1(\cX_1)] \cdots \E[\varphi_n(\cX_n)]$
diff --git a/semester4/ps/ps-jh/parts/03_expected-value/04_inequalities.tex b/semester4/ps/ps-jh/parts/03_expected-value/04_inequalities.tex
new file mode 100644
index 0000000..1a39fea
--- /dev/null
+++ b/semester4/ps/ps-jh/parts/03_expected-value/04_inequalities.tex
@@ -0,0 +1,6 @@
+\subsection{Ungleichungen}
+\shorttheorem[Markow] $\cX$ n.-neg., $g : \cX(\Omega) \rightarrow [0, \8)$. $\forall c \in \R$ mit $g(c) > 0$ gilt $\P[\cX \geq c] = \frac{\E[g(\cX)]}{g(c)}$
+
+\shorttheorem[Jensensche] $\varphi: \R \rightarrow \R$ konvex, und falls $\E[\varphi(\cX)]$ und $\E[\cX]$ wohldefiniert: $\varphi(\E[\cX]) \leq \E[\varphi(\cX)]$
+
+\shorttheorem[Dreieck] $\varphi(x) = |x|$, dann $|\E[\cX]| \leq \E[|\cX|]$. $\varphi(x) = x^2$, dann $\E[|\cX|] \leq \sqrt{\E[\cX^2]}$
diff --git a/semester4/ps/ps-jh/parts/03_expected-value/05_variance.tex b/semester4/ps/ps-jh/parts/03_expected-value/05_variance.tex
new file mode 100644
index 0000000..f82fb7b
--- /dev/null
+++ b/semester4/ps/ps-jh/parts/03_expected-value/05_variance.tex
@@ -0,0 +1,2 @@
+\subsection{Varianz}
+\shortdefinition $\cX$ mit $\E[\cX^2] < \8$
diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf
index 425f9f2..35ba265 100644
Binary files a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf and b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf differ
diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex
index d504513..91c15d3 100644
--- a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex
+++ b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.tex
@@ -64,6 +64,9 @@
 \input{parts/03_expected-value/00_intro.tex}
 \input{parts/03_expected-value/01_disc.tex}
 \input{parts/03_expected-value/02_cont.tex}
+\input{parts/03_expected-value/03_properties.tex}
+\input{parts/03_expected-value/04_inequalities.tex}
+\input{parts/03_expected-value/05_variance.tex}
 % \input{parts/03_expected-value/}