Inferential Statistics Theory of Estimators

Let X ~ POI (mu), and let theta = P[X = 0] =.

(a) Is =an unbiased estimator of theta?

(b) Show that 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 tilde for estimating theta = e^-mu when mu = 1 and mu = 2.