QUESTION 2 [12] Suppose a time series of size 50 follows x, = u+z, -z,_, process, where z, ~ WN(u,1) 20?, k = 0 1, k =0 x, = 0.157, yx = -o., k=1 and Pk k = 1 2 0 otherwise 0 otherwise (a) Calculate the variance of the estimated mean for (x, ). (b) Construct an approximate 99% confidence interval for u . (c) Are the data computable with the hypothesis that / = 0? (d) Justify your answer in part (c)