Given a random sample of size n from a Poisson distribution, lambda hat_1 = X_1 and lambda hat_2 = Xbar are two unbiased estimators for lambda. Calculate the relative efficiency of lambda hat_1 to lambda hat_2.
I know this means to campare the two variances. In other words,
Var(lambda hat_2)/Var(lambda hat_1). I'm not sure how to find the variances though. According to my formula sheet, the variance of a Poisson distribution is just lambda, and the mean of a Poisson distribution is also lambda. I guess I'm not sure how to put it all together. Any ideas?