Let m = mean
Let X ~ POI (m), and let theta = P[X = 0] = e^(-m).
a) Is theta(hat) = e^(-X) an unbiased estimator of theta?
b) Show that theta~ = u(X) is an unbiased estimator of theta, where u(0) = 1 and u(x) = 0 if x =1,2, ...
c) Compare the MSEs of theta(hat) and theta~ for estimating theta = e^(-m) when m=1 and m=2