Question

3. Let $X_{i}$ ,..., $X_{n}$ be independent random sample from N($\theta,\theta ^{2}$), where $\theta$ is unknown.

(i) Find a sufficient statistic of $\theta$.

(ii) Find the MLE of $\theta$.

(iii) Find a pivotal quantity and use it to construct a 100(1–$\alpha$)% confidence interval for $\theta$.

Answer 1

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