Answer to Question #49954 in Statistics and Probability for Jween

Question

The signals x(t) and y(t) are the input and output to linear time-invariant system with impulse response h(t),with mean and autocorrelation function given E{h}=[e^(-2t) u(t)] ,Rhh(T) = 0.5 e^(-2|t|),the random variable x(t) has a mean and autocorrelation function given by E[X]=2, Rxx(t)=0.5 e^(-2|t|). Assume the random process x(t) and h(t) are independent random processes

a. find the mean of the output random process (t), E[Y(T)] .
B.Find the auto correlation function of the random process (t), Ryy(t,u).
c. Is the output random process Y(t),wide-sense stationary?Justify
D. Find fx1x2 (x1 x2),where X1=X(0), X2=X(4)