1. Let X1, ... , Xn be a random sample from n(u, o), where both - 0 are unknown parameters. Let X = the sample mean, V = [h=(X; X)and $2 = V/(n-1), the sample variance. For parts (b) and (c), you may use the distribution of X and Q derived earlier in HW 1). (a) Show that T = (X, S) is a sufficient statistic. (b) Derive E(S) and give an unbiased estimator of 03 (c) Derive E[X/S). 1. Let X1, ... , Xn be a random sample from n(u, o), where both - 0 are unknown parameters. Let X = the sample mean, V = [h=(X; X)and $2 = V/(n-1), the sample variance. For parts (b) and (c), you may use the distribution of X and Q derived earlier in HW 1). (a) Show that T = (X, S) is a sufficient statistic. (b) Derive E(S) and give an unbiased estimator of 03 (c) Derive E[X/S)