You are given that Y has the Γ(n, θ) distribution, and hence E[Y] = n/θ and var(Y) = n/θ2. Find optimal estimators of n/θ and n/θ2. State the type of optimality.
The Rao- Blackwell theorem enables us to obtain MVU estimator through sufficient statistic. The solution contains an application of Rao-Blackwell theorem using a Gamma density.