rework for ws19/20 #6

rossmeier · 2020-01-22T20:14:48Z

thielpa · 2020-02-10T00:02:32Z

StochastischeSignale.tex

+	\textbf{Lösung:}\\
+	$\alpha = \dfrac{E[\X\Y]-E[\X]E[\Y]}{E[\X^2]-E[\X]^2} = \dfrac{c_{\X,\Y}}{\sigma^2_{\X}} = \dfrac{c_{\X,\Y}}{\sigma^2_{\X}}\dfrac{\sigma_{\Y}}{\sigma_{\Y}} = \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}$\\
+	$\beta = E[\Y] - \alpha E[\X] = E[\Y] - \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}E[\X]$\\
+	$\Rightarrow \hat{\Y} = \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}(\X-E[\X])+E[\Y]$


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thielpa · 2020-02-10T00:04:15Z

StochastischeSignale.tex

+	\begin{itemize}
+	\item $\X_n\xrightarrow{\text{a.s.}}\X \Rightarrow \X_n\xrightarrow{\text{p.}}\X$
+	\item $\X_n\xrightarrow{\text{m.s.}}\X \Rightarrow \X_n\xrightarrow{\text{p.}}\X$
+	\item $P(\{|\X_n|\leq\Y\}) = 1 \forall n \wedge E[Y^2]<\infty\wedge \X_n\xrightarrow{\text{p.}}\X \Rightarrow \X_n\xrightarrow{\text{m.s.}}\X$


Add line break before right arrow

rework for ws19/20

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rossmeier requested a review from thielpa January 22, 2020 20:14

thielpa requested changes Feb 10, 2020

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rework for ws19/20 #6

rework for ws19/20 #6

rossmeier commented Jan 22, 2020

thielpa Feb 10, 2020

thielpa Feb 10, 2020

rework for ws19/20 #6

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rework for ws19/20 #6

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rossmeier commented Jan 22, 2020

thielpa Feb 10, 2020

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thielpa Feb 10, 2020

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