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| author | Gloria Mundi <gloria@gloria-mundi.eu> | 2024-11-16 15:39:23 +0100 |
|---|---|---|
| committer | Gloria Mundi <gloria@gloria-mundi.eu> | 2024-11-16 15:39:23 +0100 |
| commit | 72bd993483453ed8ebc462f1a33385cd355d486f (patch) | |
| tree | c5592ba1ed2fed79e26ba6158d097c9ceb43f061 /content/math/tables/probability.tex | |
| parent | 98567ec798aa8ca2cfbcb85c774dd470f30e30d4 (diff) | |
| parent | 35d485bcf6a9ed0a9542628ce4aa94a3326d0884 (diff) | |
merge mzuenni changes
Diffstat (limited to 'content/math/tables/probability.tex')
| -rw-r--r-- | content/math/tables/probability.tex | 17 |
1 files changed, 7 insertions, 10 deletions
diff --git a/content/math/tables/probability.tex b/content/math/tables/probability.tex index f265d10..29f92e1 100644 --- a/content/math/tables/probability.tex +++ b/content/math/tables/probability.tex @@ -1,19 +1,15 @@ -\begin{tabularx}{\linewidth}{|LICIR|} +\begin{expandtable} +\begin{tabularx}{\linewidth}{|LIR|} \hline - \multicolumn{3}{|c|}{ + \multicolumn{2}{|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. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ & - $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\ + $\E(X + Y) = \E(X) + \E(Y)$ & $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ \\ + $\E(\alpha X) = \alpha \E(X)$ & $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\ + $X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$ & $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$\\ \hline \end{tabularx} -\vfill \begin{tabularx}{\linewidth}{|Xlr|lrX|} \hline \multicolumn{6}{|c|}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\ @@ -25,3 +21,4 @@ $\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ & \\ \hline \end{tabularx} +\end{expandtable} |
