diff --git a/mb/Uebung1.pdf b/mb/Uebung1.pdf index 64f44e8..99a6421 100644 --- a/mb/Uebung1.pdf +++ b/mb/Uebung1.pdf Binary files differ diff --git a/mb/Uebung1.tex b/mb/Uebung1.tex index f7c9509..8526c57 100644 --- a/mb/Uebung1.tex +++ b/mb/Uebung1.tex @@ -196,7 +196,7 @@ \end{pmatrix}\\$ \item $ N(\mu,\Sigma) = \frac{1}{(2\pi)^(\frac{\pi}{2})|\Sigma|^(\frac{1}{2})}e^{(-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu) )}\\ - |\Sigma_S|= \frac{264}{25}\\ + |\Sigma_S|= \frac{264}{25}\\%TODO: wrong exponents? \Sigma^{-1} = \begin{pmatrix} \frac{61}{99}&\frac{-31}{132}&\frac{-53}{198}\\ @@ -215,26 +215,43 @@ 2\\3 \end{pmatrix}\\ \Sigma_y=\begin{pmatrix} -0,5&1\\2&0.5 +1&0.5\\0.5&2 \end{pmatrix}\\$ \item $\mu_y=\begin{pmatrix} 4\\-2 \end{pmatrix}\\ \Sigma_y=\begin{pmatrix} --2&4\\8&-2 +4&-2\\-2&8 \end{pmatrix}\\$ \item$ \mu_y=\begin{pmatrix} \frac{2}{\Delta t}\\\frac{1}{\Delta t} \end{pmatrix}\\ \Sigma_y=\begin{pmatrix} -\frac{1}{2\Delta t^2}&\frac{1}{\Delta t^2}\\ -\frac{2}{\Delta t^2}&\frac{1}{2\Delta t^2} +\frac{1}{(\Delta t)^2}&\frac{1}{2(\Delta t)^2}\\ +\frac{1}{2(\Delta t)^2}&\frac{2}{(\Delta t)^2} \end{pmatrix}\\$ -\item $\mu_y=?\\ -\Sigma_y=?$ +\item $\mu_y=2\mu_x+3\mu_z=\begin{pmatrix} + 4\\2 +\end{pmatrix}+3\mu_z\\ +\Sigma_y=\begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}\begin{pmatrix} + 1&0.5\\0.5&2 +\end{pmatrix}\begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}+\begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}\Sigma_z \begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}=\begin{pmatrix} + 4&2\\2&8 +\end{pmatrix}+\begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}\Sigma_z \begin{pmatrix} + 2&0\\0&2 +\end{pmatrix}$ \end{enumerate} - %TODO Aufgaben bearbeiten \end{document}