5.22 Let X1,...,Xn be a sample from the Poisson () distribution truncated on the left at 0,...

5.22 Let X1,...,Xn be a sample from the Poisson (λ) distribution truncated on the left at 0, i.e., with sample space X = {1, 2, 3,...} (see Problem 3.20). Show that the Cramer-Rao lower bound for the variance of unbiased estimators of ´ λ is

λ(1 − e−λ)

2 n(1 − e−λ − λe−λ)

and is not attained by the UMVU estimator. (It is, however, the asymptotic variance of the ML estimator.)