Poisson distribution and unbiased estimator
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I'm stuck on this problem and I was wondering if someone could help me out. My initial guess is that if you set e^-cY equals to e^-theta => you'll get that e^-c(ntheta) = e^-theta => c = 1/n. However, I'm not sure that this is right for a. I have no idea how to begin B and C, but I know that 1/n goes to zero as n -> infinity.
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Solution Summary
The solution involves the unbiased estimator of Exp[-theta] of Poisson distribution.
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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 ...
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