diff --git a/is/UB1/ISUB1.pdf b/is/UB1/ISUB1.pdf index a7117b9..341cce9 100644 --- a/is/UB1/ISUB1.pdf +++ b/is/UB1/ISUB1.pdf Binary files differ diff --git a/is/UB1/ISUB1.tex b/is/UB1/ISUB1.tex index e0a6a4c..a3e69b8 100644 --- a/is/UB1/ISUB1.tex +++ b/is/UB1/ISUB1.tex @@ -69,7 +69,7 @@ %Kommando für Aufgaben %\Aufgabe{AufgTitel}{Punktezahl} \newcommand{\Aufgabe}[2]{\stepcounter{n} - \indent\textbf{Exercise \arabic{n}: #1} (#2 Punkte)\\} + \indent\textbf{Exercise \arabic{n}: #1} (#2 Points)\\} @@ -90,7 +90,10 @@ $\mathds{P}(2\ pairs)=\frac{123552}{2598960}=\frac{198}{4165}\approx 0.0475$ \item \begin{enumerate}[(a)] \item hands with exaclty two pairs without Spades: ${13\choose 2}{3\choose 2}^2\cdot 11\cdot 3=23166$\\ - $\mathds{P}(2\ pairs|\neg Spades)=\frac{23166}{2598960}=\frac{297}{33320}\approx 0.00891$ + $\mathds{P}(2\ pairs|\neg Spades)=\frac{23166}{2598960}=\frac{297}{33320}\approx 0.00891$\\ + one pair:\\ + ${13\choose 1}{3\choose 2}{12 \choose 3}\cdot 3^3=231660$\\ + $\mathds{P}(1\ pair|\neg Spades)=\frac{231660}{2598960}=\frac{297}{3332}\approx 0.0891$ \item $A:=2\ pairs,\ B:=\neg Spades$\\ $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$\\ $P(A)=\frac{198}{4165},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\ @@ -108,6 +111,8 @@ 1 & if\ x>\sqrt{2} \end{cases}$ \end{enumerate} - + \Aufgabe{Keep Rolling!}{4} + $\mathds{E}(X)=\frac{1}{\frac{1}{6}}=6$ (geometric distribution)\\ + $\mathds{E}(X)=?$%TODO \end{document}