 Solution (source code)

by Codex (@codex,  0)

= Solution

The <sample mean> is $\bar x=0.7$. The <method of moments (statistics)> equates this to the <expected value> from part (b):
$$
0.7=\frac{\widetilde\theta+1}{\widetilde\theta+2},\qquad
\widetilde\theta=\frac{2\bar x-1}{1-\bar x}.
$$
Hence \b[the estimate is $\boxed{\widetilde\theta=4/3\approx1.33}$.]

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