No. 8 Let X1, X2, ... be random samples from N1(0, 1). Moreover let Y's be random variables that are independent of { Xn}n=1,2,..., and satisfying that P(Yn = 1) = n 2=1 -P(Yn =0), n=1, 2, .... (1) Let On be a maximum likelihood estimator of 0 by X1, ..., Xn. Give the distribution of Vn(On - 0). You do not need to give the reason. (2) Using On given in (1), we put Zn = (1 - Yn) On + vn Yn. Give the limit of variance: 82 : = lim Var (vn(Zn -0)) (3) Let o' be the asymptotic variance of vn(Zn - 0) as n - co. Whichi is larger, of or 02 in (2)