Any help is much appreciated..
Show that the estimator X(y) is asymptotically efficient?
sum is from i=1 to n
Are the Xi's following Poisson distributions ?
You have to prove that while n goes to infinity, the variance of X(y) attains the Cramer-Rao bound. I don't know if there's an easier way...
you could prove that X(y) is the UMVUE for a Poisson distribution and hence is efficient, but it depends on what you're starting from...
Try to do it !