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, ACF
Determine the expected absolute deviation
I have no idea where to begin except maybe setting, but then I have to figure out what the PDF
is and I'm not sure how to proceed.
Determine the expected absolute deviation
I have no idea where to begin except maybe setting
The solution is that since X(t) is a Gaussian process, all linear combinations of X(t) are also Gaussian processes. That means that the PDFsince
, and the variance can be determined like this:
![Var(Y(t))=E\left\{ (Y(t)-m_Y)^2\right\}=E\left\{ \[Y(t)\]^2\right\}=E\left\{ (X(t+1)-X(t))^2\right\}=E\left\{(X(t+1))^2\right\}-2E\left\{ X(t+1)X(t)\right\}+E\left\{ (X(t))^2\right\}=2r_X(0)-2r_X(1)=1](http://latex.codecogs.com/png.latex?Var(Y(t))=E\left\{ (Y(t)-m_Y)^2\right\}=E\left\{ \[Y(t)\]^2\right\}=E\left\{ (X(t+1)-X(t))^2\right\}=E\left\{(X(t+1))^2\right\}-2E\left\{ X(t+1)X(t)\right\}+E\left\{ (X(t))^2\right\}=2r_X(0)-2r_X(1)=1)
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