Probability involving Gaussian random sequences

[ashah99]

Homework Statement

Please see below.

Relevant Equations

PSD, autocorrelation function

How do I approach the following problem while only knowing the PSD of a Gaussian random sequence (i.e. I don't know the exact distribution of $V_k$)? Or am I missing something obvious?

Problem statement:

Thoughts:
I know with the PSD given, the autocorrelation function are delta functions due to a white process, such that it takes a value of 20 at k = 0 and value of 8 at k = +1 and -1. Any ideas?

 

[lippyka]

To approach this problem, you need to use the fact that the PSD of a Gaussian random sequence is the Fourier transform of its autocorrelation function. Thus, you can use the given PSD to calculate the autocorrelation function, and then use this to solve for the distribution of $V_k$.