Cramer Rao Bound
Consider a random sample of size n from a Poisson distribution, Xi ~ POI (
).
(a) Find the CRLB for the variances of unbiased estimators of
(b) Find the CRLB for the variances of unbiased estimators of
.
(c) Find a UMVUE of .
(d) Find the MLE 
of
.
(e) Isan unbiased estimator of?
(f) Isasymptotically unbiased?
(g) Show that
is an unbiased estimator of theta.
(h) Find Var (
) and compare to the CRLB of (b).
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