# Second moments (i.e E[X^2]) for this WSS random process

I've attempted the question, please see attached image of my working out and solution to the question. My main question is how to go from the last line of my working out to “2Rx(0) - 2Rx(t) in the solution"

Please could you help me in understanding how to work out the solutions to this question regarding second moments (i.e E[X^2]) for the WSS random process

Many Thanks

• Why did you post the same question twice? – Matt L. Jun 1 '17 at 13:13
• Apologies, I rushed the previous upload (did not include my workings) hence someone commented to remove the post. Therefore I uploaded again as I despereatly need help in the question – Arsenal123 Jun 1 '17 at 14:40

## 1 Answer

$X(t)$ is a wide-sense stationary (WSS) process, so its first and second moments are independent of time. Consequently, $E[X^2(t)]$ has the same value for any value of $t$:

$$E[X^2(t)]=E[X^2(t+\tau)]=R_X(0)$$

That's how you get the term $2R_X(0)$ in the solution.

• @Arsenal123: Great. In that case you can accept / upvote the answer. – Matt L. Jun 1 '17 at 16:43