Let X1,...,Xn be a random sample from the Poisson distribution with unknown mean . The uniformly minimum variance unbiased estimator (UMVUE) of exp() is known

Let X1,...,Xn be a random sample from the Poisson distribution with unknown mean λ. The uniformly minimum variance unbiased estimator

(UMVUE) of exp(−λ) is known to be [(n − 1)/n]

Tn , where Tn = n i=1 Xi. Find the asymptotic distribution of the UMVUE (appropriately normalized). Hint: It may be easier to first find the asymptotic distribution of exp(−Tn/n).