Suppose thatX1,X2,...,Xn are Independent and identically distributed N(,2) for someR and 2(0,). Let T=(X)/(S/n), where Xand S have their usual meanings. Assume that n is large enough for all expectations and variances below to exist. a) Identify the conditional distribution of T given thatS=s(0,) b) Use Jensen's inequality to show that E[2/S2]=1. b) Use the kernel method to calculate E[2/S2]. c) Find find Var[T]. [Intuitively, replacing the constant in(X)/(/n) withS increases variability.] e) How large did n need to be ?