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authormzuenni <michi.zuendorf@gmail.com>2024-09-08 22:16:36 +0200
committermzuenni <michi.zuendorf@gmail.com>2024-09-08 22:16:36 +0200
commit45d95c45013bf4ff73570c94c58b7f0212ccdf26 (patch)
treee47f9b16f44acef5f2517655fe2a16f8108f5af1 /content/math/tables/probability.tex
parentdf963645ca0c5d0bed4fb9c02e93233dcfd53dae (diff)
moved stuff
Diffstat (limited to 'content/math/tables/probability.tex')
-rw-r--r--content/math/tables/probability.tex17
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}