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 PDF is also a standard Gaussian PDF. since , and the variance can be determined like this:
is a Gaussian stochastic process with mean , 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.
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 PDF is also a standard Gaussian PDF. since , and the variance can be determined like this: