Suppose that X1, X2 , … , Xn form a random sample from a Poisson
distribution with unknown mean θ, and let Y = ∑i=1 Xi.
A) Determine the value of a constant c such that the
estimator e-cY is an unbiased estimator of e-θ
B) What is the lower bound for the variance of the unbiased
estimator found in part (a)?
C) Suppose that we wish to estimate 1/ θ. Consider n/(Y+1)
as an estimator of θ. Find the bias of this estimator, and show that
the bias goes to 0 as n → ∞. Prove that there is no unbiased
estimator of 1/ θ.