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diff --git a/content/math/tables/probability.tex b/content/math/tables/probability.tex new file mode 100644 index 0000000..f265d10 --- /dev/null +++ b/content/math/tables/probability.tex @@ -0,0 +1,27 @@ +\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. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$\\ + + $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ & + $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ & + $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\ + \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} |