diff --git a/UBVorlage.tex b/UBVorlage.tex index 543fe54..6e2dc04 100644 --- a/UBVorlage.tex +++ b/UBVorlage.tex @@ -69,9 +69,7 @@ %Kommando für Aufgaben %\Aufgabe{AufgTitel}{Punktezahl} \newcommand{\Aufgabe}[2]{\stepcounter{n} -\begin{equation} - -\end{equation}\textbf{Aufgabe \arabic{n}: #1} (#2 Punkte)\\} + \textbf{Aufgabe \arabic{n}: #1} (#2 Punkte)\\} diff --git a/is/UB1/ISUB1.pdf b/is/UB1/ISUB1.pdf deleted file mode 100644 index 8820c27..0000000 --- a/is/UB1/ISUB1.pdf +++ /dev/null Binary files differ diff --git a/is/UB1/ISUB1.tex b/is/UB1/ISUB1.tex index 9deb47d..73878a2 100644 --- a/is/UB1/ISUB1.tex +++ b/is/UB1/ISUB1.tex @@ -99,7 +99,7 @@ \item $A:=1\ pair,\ B:=\neg Spades$\\ $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$\\ $P(A)=\frac{352}{833},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\ - $P(B|A)=1-P(\neg B| A)=1-\left(\frac{1}{4}+\frac{3}{4}\frac{1}{4}+\left(\frac{3}{4}\right)^2\frac{1}{4}+\left(\frac{3}{4}\right)^3\frac{1}{4}+\left(\frac{3}{4}\right)^4\frac{1}{3}\right)=1-\frac{101}{128}=\frac{27}{128}\approx 0.211$\\ + $P(B|A)=1-P(\neg B| A)=1-\left(\frac{1}{4}+\frac{3}{4}\cdot\frac{1}{4}+\left(\frac{3}{4}\right)^2\frac{1}{4}+\left(\frac{3}{4}\right)^3\frac{1}{4}+\left(\frac{3}{4}\right)^4\frac{1}{3}\right)=1-\frac{101}{128}=\frac{27}{128}\approx 0.211$\\ $P(A|B)=\frac{\frac{27}{128}\cdot \frac{352}{833}}{\frac{2109}{9520}}=\frac{1980}{4921}\approx 0.402$ \item $A:=2\ pairs,\ P(A)=\frac{198}{4165}$, B as above\\ $P(B|A)=1-\left(\frac{1}{4}+\frac{3}{4}\cdot\frac{1}{4}+\left(\frac{3}{4}\right)^2\cdot\frac{1}{4}+\left(\frac{3}{4}\right)^3\cdot\frac{1}{3}+\left(\frac{3}{4}\right)^3\frac{2}{3}\cdot\frac{1}{3}\right)=\frac{3}{16}$\\ @@ -122,7 +122,7 @@ 0 & if\ z<0\\ \frac{1}{2} z^2 & if\ 0\leq z\leq \sqrt2\\ 1 & if\ z>\sqrt2 - \end{cases}$%TODO: adjust intervals dazu sagt das Beispiel nichts... + \end{cases}$ \\ reference: http://math.arizona.edu/$\sim$jwatkins/f-transform.pdf \end{enumerate} \Aufgabe{Keep Rolling!}{4} diff --git a/mb/Rechnung3c.mn b/mb/Rechnung3c.mn index 9ee4ec0..fc4b023 100644 --- a/mb/Rechnung3c.mn +++ b/mb/Rechnung3c.mn Binary files differ