### Unbiased estimator of theta

Assignment Help Basic Statistics
##### Reference no: EM1387848

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

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