From 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Mon, 27 Jun 2022 17:19:28 +0200
Subject: updated tcr

---
 math/tables/probability.tex | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 math/tables/probability.tex

(limited to 'math/tables/probability.tex')

diff --git a/math/tables/probability.tex b/math/tables/probability.tex
new file mode 100644
index 0000000..4f72707
--- /dev/null
+++ b/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. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$\\
+	
+	$\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ &
+	$\Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ &
+	$\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\
+	\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}
-- 
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