Solved: Consider a random sample of size n from a poisson, Basic Statistics

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Consider a random sample of size n from a poisson

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.

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Basic Statistics: Consider a random sample of size n from a poisson

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