Textbook Exercise 4.2

[homerhanumat]

It seems that the problem should be to explain why the first moment is not useful. After all:

\begin{aligned}
  \sigma^2 &\approx s^2 \frac{n}{n-1},\\
  \frac{(\theta - - \theta)^2}{12} &\approx s^2 \frac{n}{n-1},\\
  \frac{4\theta^2}{12} &\approx s^2 \frac{n}{n-1},\\
  \theta &\approx \sqrt{\frac{3n}{n-1}} s,\\
  \hat{\theta} &= \sqrt{\frac{3n}{n-1}} s.
\end{aligned}

[rpruim]

Yes, we just talked about this in class this week. I guess the question is what one defines as the method of moments.

[rpruim]

I'll likely add a comment to the solution to make sure it is clear that a second moment might be useful.