- Let X1,..., Xn be an i.i.d. sample from the uniform distribution on [0 1,0 + 1]. = With U max{X1,..., Xn} and V = min{X1,..., Xn), any value between U - 1 and V + 1 is an mle for 0. In particular, consider 0 =U-1 and 02 (U - 1) + (V + 1) U + V = = 2 2 1. Find the bias, the variance, and the mean squared error of . Hint: Let Y = {X; - (0 - 1)}/2. Then Y,..., Y are i.i.d. uniform on [0,1]. The mean and variance of max{Y,..., Yn} are given by Problem 20 (with 0 = 1). 2. Find the bias, the variance, and the mean squared error of 2. Hint: The density function of 2 is 2(x) = - [(n/2){x (0 1)}n1, 0 1 x 0, ((n/2){(0 + 1) x}"1, 0x0+1.