1. Let X1, . .., Xn be iid with pdf f (x| 01, 02) = -e-(2-01)/02, 2 > 01, - 00 0. Show that (Xn - X1)/(X2 - X1) is an ancillary statistic for 01 and 02. 2. Investigate complete sufficiency when a random sample of size n is taken from (a) Poisson (1) (b) Gamma(p, 0) 3. Let X1, . . . , Xn be iid with exponential distribution with mean 0. Show that (XitX2)/ Ci-1 Xi and Eil Xi are independent. 4. Let X1, . . . , X4 be iid Unif(0, 0). (a) Show that X(4) is independent of X(1) / X(4). (b) Show that X(4) is independent of (X(1) + X(2))/ (X(3) + X(4)). 5. Let Y be the nth order statistic of a random sample of size n from Unif(0, 0). Let 0 has the prior pdf h(0) = Bab /08+1, 0 > a > 0, where a > 0, B > 0. Find the Bayes estimator of 0 under the squared error loss. 6. Let X1, . .. , Xn be iid Poisson(0). Assume the prior distribution on 0 is Gamma(a, 1/c) with pdf * (0 ) = r(a) ga-le-co , 0 > 0 . Find the Bayes estimator of 0 under a squared error loss