= 2. Let X (X1, X2,..., Xn) denote a random sample of size n from the Poisson distribution with mean 0, where the parameter 0 > 0 is unknown. Consider the statistic n T(X) = X. i=1 (i) Show that T has a Poisson distribution with mean no. (ii) By showing that the conditional distribution of X given T is multinomial and does not depend upon 0, deduce that T is sufficient for 0. Use the Factorization Theorem to provide another proof that T is sufficient for .