Suppose that Yt follows the stationary AR(1) model Y t = XXXXXXXXXX7Y t - 1 + u t , where u t is i.i.d. with E(u t ) = 0 and var1ut2 = 9. a. Compute the mean and variance of Y t . b. Compute the first...

Suppose that Yt follows the stationary AR(1) model Y_t = 2.5 + 0.7Y_{t - 1} + u_t,
where u_t is i.i.d. with E(u_t) = 0 and var1ut2 = 9.
a. Compute the mean and variance of Y_t.
b. Compute the first two autocovariances of Y_t.
c. Compute the first two autocorrelations of Y_t.

d. Suppose that Y_T = 102.3. Compute Y_T+1|T = E(Y_T+1 |Y_T, Y_{t - 1}, . . . . ).