Question
Let $X_{1}, X_{2}, \ldots, X_{n}$ denote a random sample from a distribution that is $N(0, \theta)$. Then $Y=\sum X_{i}^{2}$ is a complete sufficient statistic for $\theta$. Find the MVUE of $\theta^{2}$.
Step 1
e., $Y \sim \chi^{2}(n)$, where $n$ is the sample size. This is because the sum of squares of $n$ independent standard normal random variables follows a chi-square distribution with $n$ degrees of freedom. Show more…
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