As above, argue that both proposed estimators 1 and 1 are consistent and asymptotically normal. Then, give their asymptotic variances V (1) and V (1)...

As above, argue that both proposed estimators 1 and 1 are consistent and asymptotically normal. Then, give their asymptotic variancesV (1) and V (1) , and decide if one of them is always bigger than the other.Let X1, ..., Xn Exp (1) , for some 1 > 0 . Let 1 =-and 1 = - In (Y n) , where Y; = 1{X; > 1},i= 1, . . .,n .XnV (1) =V (i) =Ov (A) > V (1) for all 2 .ov (1) < V (1) for all 2 .O V (x) = V (1) for all 2 .O There exists 11 such that V (1) > V (1) and 12 such that V ( ") < V (1)