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.
Please see the attached file.
Rao- Blackwell theorem
If is a sufficient statistic for and is unbiased for , then there is a function of namely which is unbiased for and has variance lesser than that of .
Thus the Rao- Blackwell theorem enables us to …
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.