I was asked a question, as posted here, and the answer given is (A) i.e. $\frac{3}{2} A^2 N_0$.
My solution steps was:
Finding the mean of the output process: Since input is gaussian the output will be also Gaussian, as per property of Gaussian variable.
Finding the mean square value (MSV) of the process i.e. $\mathbb{E}(Y^2)$.
Variance = MSV$-\mathbb{E}(Y)^2$
But I am confused do mean of output process will be zero? Since the input is zero-mean white Gaussian noise if yes how?
Is there any other way to solve the question?