[PS] Add more notes

semester4/ps/ps-jh/parts/03_expected-value/03_properties.tex

@@ -16,3 +16,6 @@ $\E\left[ \prod_{k = 1}^n \cX_k \right] = \prod_{k = 1}^n \E[\cX_k]$
 
 \shorttheorem äquivalent: \bi{(1)} $\cX_i$ unabhängig,\\
 \bi{(2)} $\forall \varphi_i$: $\E[\varphi_1(\cX_1) \cdots \varphi_n(\cX_n)] = \E[\varphi_1(\cX_1)] \cdots \E[\varphi_n(\cX_n)]$
+
+\shortremark[Bedingte W.] $\E[I] = \P[K \cap R]\E[I | K, R] + \ldots$\\
+{\scriptsize Dabei beinflussen $K$ und $R$ den Wert nur durch Bedingte W.}

semester4/ps/ps-jh/parts/03_expected-value/05_variance.tex

@@ -1,6 +1,4 @@
 \subsection{Varianz}
-$\E[\cX^2] = \sum_{x \in W} x^2 \cdot p_\cX(x)$ ($\cX$ diskret)
-
 \shortdefinition $\cX$ mit $\E[\cX^2] < \8$, $\V[\cX] = \E[(\cX - \E[\cX])^2]$
 
 \shortdefinition[Standardabweichung] $\sigma(\cX) = \sqrt{\V[\cX]}$