(1} Consider the MA{ 1} process X.\" 2 an + sans, an N man, (a) Denote the heat linear predictor of Xn+1 using the DurbinIevinson algorithm as fin+1 = {111,an + ,2-Xnl + . . . + cam-1X1- Use mathematical induction to prove that 3,311 = parts-\"(1 + a\" + + awn-21mm, an,\" = {a}\";{1 + a? + + HEW}. {h} Find the partial autocorrelation function of 1]1 {2(2) and (2(3). Hint: Induction consists of two steps. The base step proves the statement for n = 1 [or another value] without an},r assumption. The second step proves that, if the statement holds for n = If, it must also hold for n. = I: + 1