Answer to Question #50066 in Complex Analysis for vallle

Question

Let x(t) be a random process defined as
x(t)=A COS [2 PI .T+ Theta],where A is a Gaussian random variable with mean E{A}=0 and variance A = 2, The random variable theta is uniform distributed on the interval [-pi,pi], which is statistically independent from A.
Define random process Z(t) given by
Z(t)=integral from 0 to 1 of X(t) dt

A. Compute the mean of Z(t), E[Z(t)]
b. Determine the variance of Z(t), vaiance z
c. Is the process Z(t) strict sense stationary ,wide sense stationary ? Justify your answer
D. Is the process X(t) Gaussian process ?