= Rao-Blackwellization of a multinomial probability product
{c}
{title2=$\widehat{p_0p_1p_2}=n_0n_1n_2/[n(n-1)(n-2)]$}
For $n\geq3$ independent labels with three type probabilities, conditioning the indicator of an ordered $(0,1,2)$ initial triple on the <multinomial distribution> type counts gives the displayed unbiased <estimator>. The <Rao-Blackwell theorem> reduces its <variance> strictly when all three probabilities are positive. At a boundary parameter with a missing type, both <variances> vanish.
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