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15
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Moments of area of random triangle inscribed in a circle
If $q$ is uniformly distributed on the unit circle, $E[q^n]=\delta_{n0}$. So if $f$ is meromorphic, $E[f(q)]$ is the constant term in $f$.
The area of triangle $pqr$ is $\frac12\Im[(q-p)(\bar{r}-\bar …