Suppose that Yt follows the stationary AR(1) model Yt = 2.5 + 0.7Yt-1 + ut, where ut

Question:

Suppose that Yt follows the stationary AR(1) model Yt = 2.5 + 0.7Yt-1 + ut, where ut is i.i.d. with E(ut) = 0 and var(ut) = 9.
(a) Compute the mean and variance of Yt.
(b) Compute the first two auto covariances of Yt.
(c) Compute the first two autocorrelations of Yt.
(d) Suppose that YT = 102.3. Compute YT+1|T = E(YT+1|YT, Yt-1...).