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authormzuenni <michi.zuendorf@gmail.com>2022-06-27 17:19:28 +0200
committermzuenni <michi.zuendorf@gmail.com>2022-06-27 17:19:28 +0200
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+\begin{tabularx}{\linewidth}{|LICIR|}
+ \hline
+ \multicolumn{3}{|c|}{
+ Wahrscheinlichkeitstheorie ($A,B$ Ereignisse und $X,Y$ Variablen)
+ } \\
+ \hline
+ $\E(X + Y) = \E(X) + \E(Y)$ &
+ $\E(\alpha X) = \alpha \E(X)$ &
+ $X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$\\
+
+ $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ &
+ $\Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ &
+ $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\
+ \hline
+\end{tabularx}
+\vfill
+\begin{tabularx}{\linewidth}{|Xlr|lrX|}
+ \hline
+ \multicolumn{6}{|c|}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\
+ \hline
+ & $\#A > k\#B$ & $Pr = \frac{a - kb}{a + b}$ &
+ $\#B - \#A \leq k$ & $Pr = 1 - \frac{a!b!}{(a + k + 1)!(b - k - 1)!}$ & \\
+
+ & $\#A \geq k\#B$ & $Pr = \frac{a + 1 - kb}{a + 1}$ &
+ $\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ & \\
+ \hline
+\end{tabularx}