rework for ws19/20 #6
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thielpa
requested changes
Feb 10, 2020
StochastischeSignale.tex
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| \textbf{Lösung:}\\ | ||
| $\alpha = \dfrac{E[\X\Y]-E[\X]E[\Y]}{E[\X^2]-E[\X]^2} = \dfrac{c_{\X,\Y}}{\sigma^2_{\X}} = \dfrac{c_{\X,\Y}}{\sigma^2_{\X}}\dfrac{\sigma_{\Y}}{\sigma_{\Y}} = \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}$\\ | ||
| $\beta = E[\Y] - \alpha E[\X] = E[\Y] - \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}E[\X]$\\ | ||
| $\Rightarrow \hat{\Y} = \rho_{\X,\Y}\dfrac{\sigma_{\Y}}{\sigma_{\X}}(\X-E[\X])+E[\Y]$ |
StochastischeSignale.tex
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| \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 $P(\{|\X_n|\leq\Y\}) = 1 \forall n \wedge E[Y^2]<\infty\wedge \X_n\xrightarrow{\text{p.}}\X \Rightarrow \X_n\xrightarrow{\text{m.s.}}\X$ |
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🤖 The artifacts from this build are available here. |
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🤖 The artifacts from this build are available here. |
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🤖 The artifacts from this build are available here. |
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🤖 The artifacts from this build are available here. |
stevensalloum
approved these changes
Mar 7, 2025
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