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7.5.10. Let $X_{1}, X_{2}, ldots, X_{n}$ be a random sample from a distribution with pdf $f(x ; theta)=theta^{2} x e^{-theta x], 0 0 .$ (a)

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7.5.10. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from a distribution with pdf $f(x ; \theta)=\theta^{2} x e^{-\theta x], 00 .$ (a) Argue that $Y=\sum_{1}^{n} X_{i}$ is a complete sufficient statistic for $\theta$. (b) Compute $E(1 / Y$ and find the function of $y$ that is the unique MVUE of $\theta$. SP.PB. 107

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