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diff --git a/math/tables/probability.tex b/math/tables/probability.tex deleted file mode 100644 index f265d10..0000000 --- a/math/tables/probability.tex +++ /dev/null @@ -1,27 +0,0 @@ -\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} |