TIME SERIES STATISTICS

QUESTION 5 (a) If X1, X2, ..., Xn are independent normal random variables, i.e., Xt ~ N(A, o?), (i) find the respective distributions of ap = E Xtcos (2upt ) and bp = = >; Xtsin (2apt ) (5) n and (ii) show that ap and bo are independent, for p = 1, ..., (n/2 ) - 1. (3)