c. Suppose X1,,Xn are i.i.d. random variables such that Xi Poisson ). Consider the statistic T=i=1nXi. Show that T is sufficient (i) using the definition of sufficiency (conditional distribution of X1=x1,,Xn=xn given T=t ) and (ii) using the factorization theorem. d. Suppose X1,,Xn are i.i.d. random variables with XiN(,1). Show that the minimum variance unbiased estimator of 2 is ^=X2n1. Find the variance of ^. Does the variance of ^ attain the lower bound for the variance of an unbiased estimator of 2 ? e. Let X1,,Xn be i.i.d. N(,) random variables. Find an unbiased estimator of 2 (denote this estimator with ^ ). What steps do we need to follow to show if ^ is an efficient estimator of 2 ?.