[PS] Start adding more expected values / variance defs

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

@@ -16,10 +16,14 @@ $\V[\cX] = \E[\cX^2] - \E[\cX]^2 = a^2\E[1_\Omega] - a^2 = 0$
 \shortproposition $\cX_k$ paarw. unabh. $\V\left[ \sum_{k = 1}^{n} \cX_k \right] = \sum_{k = 1}^{n} \V[\cX_k]$.
 Falls $\cX_k$ abhängig, dann gilt $\neq$
 
+\newpage
 \shortexample Varianz von bekannten Verteilungen
 \begin{itemize}
     \item $\cX \sim \text{Ber}(p)$, $\V[\cX] = p (1 - p)$
     \item $\cX \sim \text{Bin}(n, p)$, $\V[\cX] = n p (1 - p)$
+    \item $\cX \sim \text{NBin}(r, p)$, $\V[\cX] = \frac{r(1 - p)}{p^2}$
+    \item $\cX \sim \text{Geom}(p)$, $\V[\cX] = \frac{1 - p}{p^2}$
+    \item $\cX \sim \text{H}(n, r, m)$, $\V[\cX] = m\frac{rn - r^2}{n^2} \frac{n - m}{n - 1}$
     \item $\cX \sim \text{Poisson}(\lambda)$, $\V[\cX] = \lambda = \E[\cX]$
     \item $\cX \sim \cU([a, b])$, $\V[\cX] = \frac{(b - a)^2}{12}$
     \item $\cX \sim \cN(\mu, \sigma^2)$, $\V[\cX] = \sigma^2$