Show that the mean of a random sample of size n is a minimum variance unbiased estimator of "lambda", of a Poisson distribution.
Can anybody provide some help for me?
You'll need to use the Lehmann–Scheffé theorem which states that if Y is a complete sufficient statistic for lambda, and there exists a function of Y such that this function is an unbiased estimator of lambda, then this function is an MVUE of lambda.
1. Find a complete sufficient statistic (Y) for lambda
2. Find a function of Y such that this function is an unbiased estimator of lambda.