Question One Let X = (X1, X2, . .., Xn) be a sample of i.i.d. Poisson(@) random variables with probability mass function f(x; 0) = Po(X = x) _ e( TE {0, 1, 2, . .. }, 020. a [2 marks] The statistic T(X) = _ _ X; is complete and sufficient for 0. Which of the following provides justification for why this statement is true. Poisson belongs to the one-parameter exponential family with a(0) = logo, b(x) = x, c(0) = e- and d(x) = Poisson belongs to the one-parameter exponential family with a(0) = loge, b(x) = , c(0) = e- and d(x) =x. Poisson belongs to the one-parameter exponential family with a(0) = e , b(x) = 1 c(0) = loge and d(x) = r.O Neyman-Fisher Factorization Criterion since f can be written as f(x; 0) = Le exp(x log 0) O Poisson belongs to the one-parameter exponential family with a(0) = e , b(x) = c(0) = 0 and d(x) =r