Please Do not Answer mistakely submitted blurr image.

Statistics and probability.

1. Let X1, X2 be a sequence of i.i.d. N (u, o ) rando ariables, where u 0 and 0 - Vn(X, -M) , where Xn = - [" Xi,n = 1,2, . .. Show that the ser ce {Zn )n1 does not have a limiting " tribution, however, the sequence . in21 has a limiting distribution. .. Let X1, X2, ... be a sequence .i.d. random variables. Let X1:n = min{X1, ..., X} and let Yn = nXin,n - , 2, .... Find the limiting distribution of {X1:n)1 and (Yn)n21 when (i) X 1 ~ Ur' J ) , 0 0 (ii) X. _xp(0), 0 0