Suppose that a random variable X has the Poisson distribution with unknown mean ( 0) Show that the only unbiased estimator of e2 is the estimator (X) such that (X) 1 if X is an even integer and (X) 1 if X is an odd integer ...

Suppose that a random variable X has the Poisson distribution with unknown mean ( > 0).

Question:

Suppose that a random variable X has the Poisson with unknown mean λ (λ > 0). Show that the only unbiased estimator of e−2λ is the estimator δ(X) such that δ(X) = 1 if X is an even integer and δ(X) = −1 if X is an odd integer.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...