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Consider a random sample of size n from a Poisson distribution, Xi ~ POI(m).

a) Find the CRLB for the variances of unbiased estimators of m.

b) Find the CRLB for the variances of unbiased estimators of theta = e^(-m).

c) Find the UMVUE of m.

d) Find the MLE theta(hat) of theta.

e) Is theta(hat) an unbiased estimator of theta?

f) Is theta(hat) asymptotically unbiased?

g) Show that theta~ = [(n-1)/n]^(sum Xi) is an unbiased estimator of theta.

h) Find Var(theta~) and compare to the CRLB of b).

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