Suppose that Y1, . .., Yn is a random sample from an Exp(B) distribution with mean B > 0 unknown. (a) Find the distribution of Y and Y(1) = min{Y1, ..., Yn}. (b) Find constants a, b, c, and d such that Ti = aY + b and T2 = cY(1) + d are unbiased estimators of B. Compare the MSE of T1 and T2- (c) Find P (Y( 1) - $ 5 2 5 ) (d) Construct a 100(1 - a)% confidence interval for B using the pivot U = 2n(1) B