Consider the random process Xt 2 A cos2pittheta where A and

Consider the random process X(t)= 2 + A* cos(2*pi*t+theta), where A and theta are independent random variables. Assume that A is a zero mean random variable with a variance of 1 and that theta is a uniformly distributed random variable on [-pi, pi].

a. Find the probabilistic mean E[X(t)] based on A and theta

b. Find the time average mean x(t)

c. Find the probabilistic 2nd moment E[X(t)^2]

d. Find the time average 2nd moment x(t)^2

e. Is the random process ergodic?

f. Find the autocorrelation of X(t).

Solution