1. [28 marks] Let X = (X1, X2, ....Xn) (n 2 2) be i.i.d. random variables having Poisson distribution with density f(r, A) = $4. I! . = 0, 1,2, ... a) Show that the product of indicators (m=0)(X) . I(12=0)(X) is an unbiased estimator of the parameter (1) = e-2 b) Given that T = >X; is complete and minimal sufficient for A, derive 1=1 the UMVUE of T(A) = e-2). (Hint: you may use part (a)). c) Does the variance of the UMVUE in b) attain the Cramer-Rao bound for the minimal variance of an unbiased estimator of T()) = e-2)? Give reasons for your