1. Let X1, . . . ,Xn be a random sample from the uniform(0,) distribution, and let!1 = 2X and!2 = X(n), that is, the

1. Let X1, . . . ,Xn be a random sample from the uniform(0,θ) distribution, and let!θ1 = 2X and!θ2 = X(n), that is, the largest order statistic, be estimators for θ. It is given that the mean and variance of!θ2 are

(a) Give an expression for the bias of each of the two estimators. Are they unbiased?

(b) Give an expression for the MSE of each of the two estimators.

(c) Compute the MSE of each of the two estimators for n = 5 and true value of θ equal to 10. Which estimator is preferable according to the MSE selection criterion?

n n Ee (2) = and Vare (2) -02. n+1 (n+1)(n+2)