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| author | Paul Jungeblut <paul.jungeblut@gmail.com> | 2016-10-30 21:25:38 +0100 |
|---|---|---|
| committer | Paul Jungeblut <paul.jungeblut@gmail.com> | 2016-10-30 21:25:38 +0100 |
| commit | 9e82d99e75b40c64fc1a12bbb4471ba7a72694fc (patch) | |
| tree | 5d769764f6bfa6df9a3283dad4fc52796177b44d | |
| parent | 7d3908db71c6a49dc9853086090e500363c0c41b (diff) | |
Adding new sections to math chapter.
| -rw-r--r-- | latexHeaders/math.tex | 2 | ||||
| -rw-r--r-- | math/math.tex | 31 | ||||
| -rw-r--r-- | tcr.pdf | bin | 268408 -> 270349 bytes |
3 files changed, 33 insertions, 0 deletions
diff --git a/latexHeaders/math.tex b/latexHeaders/math.tex index 87a90a4..9949002 100644 --- a/latexHeaders/math.tex +++ b/latexHeaders/math.tex @@ -58,3 +58,5 @@ \end{matrix} \biggr\} } +% Expectation values. +\newcommand{\E}{\text{E}} diff --git a/math/math.tex b/math/math.tex index e2cb565..f253622 100644 --- a/math/math.tex +++ b/math/math.tex @@ -316,6 +316,37 @@ Anzahl der Teilmengen von $\mathbb{N}$, die sich zu $n$ aufaddieren mit maximale } \\ \bottomrule \end{tabular} +\vspace{5mm} + +\begin{tabular}{l|r} + \toprule + \multicolumn{2}{c}{ + Wahrscheinlichkeitstheorie ($A,B$ Ereignisse und $X,Y$ Variablen) + } \\ + \midrule + $\E(X + Y) = \E(X) + \E(Y)$ & + $\E(\alpha X) = \alpha \E(X)$ \\ + + $X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$ & + $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ \\ + + $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ & + $\Pr[A \land B] = \Pr[A] \cdot \Pr[B]$ \\ + \bottomrule +\end{tabular} +\vspace{5mm} + +\begin{tabular}{lr|lr} + \toprule + \multicolumn{4}{c}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\ + \midrule + $\#A > k\#B$ & $Pr = \frac{a - kb}{a + b}$ & + $\#B - \#A \leq k$ & $Pr = 1 - \frac{a!b!}{(a + k + 1)!(b - k - 1)!}$ \\ + + $\#A \geq k\#B$ & $Pr = \frac{a + 1 - kb}{a + 1}$ & + $\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ \\ + \bottomrule +\end{tabular} \subsection{Satz von \textsc{Sprague-Grundy}} Weise jedem Zustand $X$ wie folgt eine \textsc{Grundy}-Zahl $g\left(X\right)$ zu: Binary files differ |
