# Rao- Blackwell Theorem

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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.

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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.

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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 ...

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