Suppose xt = m + wt + qwt1, where wt ? wn(0, s2w ). (a) Show that mean function is E(xt) = m. (b) Show that the autocovariance function of xt is given by gx(0) = s2w (1 + q2), gx(?1) = s2w q, and gx(h) = 0 otherwise.(c) Show that xt is stationary for all values of q 2 R.(d) Use (2.20) to calculate var( ¯ x) for estimating m when (i) q = 1, (ii) q = 0, and (iii) q = 1 (e) In time series, the sample size n is typically large, so that (n1) n ?1. With this as a consideration, comment on the results of part (d); in particular, how does the accuracy in the estimate of the mean m change for the three different cases?