(Solution Library) Let X ~ POI (mu), and let theta = P[X = 0] = e^-mu. Is theta hat = e^-X an unbiased estimator of theta? Show that theta tilde = U(X) is an unbiased

Question: Let X ~ POI (mu), and let theta = P[X = 0] = e^-mu.

Is theta hat = e^-X an unbiased estimator of theta?
Show that theta tilde = U(X) is an unbiased estimator of theta, where u(0) = 1 and u(x) = 0 if x = 1,2,…..
Compare the MSEs of theta hat and theta tilde for estimating theta = e^-mu when mu = 1 and mu = 2.

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(Solution Library) Let X ~ POI (mu), and let theta = P[X = 0] = e^-mu. Is theta hat = e^-X an unbiased estimator of theta? Show that theta tilde = U(X) is an unbiased

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