# Poisson distribution and unbiased estimator

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.

See attached file for full problem description.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:54 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/poisson-distribution-unbiased-estimator-131271

#### Solution Preview

Please see the attached file.

Suppose that X1, X2 , ... , Xn form a random sample from a Poisson distribution with unknown mean Î¸, and let Y = âˆ‘i=1 Xi.

A) Determine the value of a constant c such that the estimator e-cY is an unbiased estimator of e-Î¸

B) What is the lower bound for the variance of the unbiased estimator found in part (a)?

C) Suppose that we wish to ...

#### Solution Summary

The solution involves the unbiased estimator of Exp[-theta] of Poisson distribution.