Method of moments for an endpoint

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Problem

A sample $2,4,3$ comes from $\operatorname{Uniform}(0,\theta)$ with $\theta>0$ . Find the one-moment method-of-moments estimate of $\theta$ .

Reveal answer or reference solution

Since $E[X]=\theta/2$ , match the population mean to the sample mean $\bar x=(2+4+3)/3=3$ . Thus $3=\hat\theta/2$ and

\hat\theta_{\mathrm{MOM}}=6

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Method of moments for an endpoint

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