Consider a random sample of size n from a Poisson distribution, Xi ~ POI(mu).
a) Find the CRLB for the variances of unbiased estimators of theta = e^(-mu).
b) Is theta(hat) an unbiased estimator of theta?
c) Is theta(hat) asymptotically unbiased?
Hint: Note that Y=SumXi~POI(n*mu), and that E(theta(tilde)) and Var(theta(tilde)) are related to the MGF of Y.