= Conditional bootstrap variance of a sample mean
{title2=$\operatorname{Var}_*(\overline a^*)=n^{-2}\sum_i(a_i-\overline a)^2$}
Conditionally on the observed values, bootstrap draws are iid from their <empirical distribution>. Each draw has <variance> $n^{-1}\sum_i(a_i-\overline a)^2$, so averaging $n$ independent draws gives the displayed <variance>. The <variance> across $B$ independent replicate means, using denominator $B-1$, is unbiased for this conditional quantity. Its expectation over the original iid data is $(n-1)\operatorname{Var}(a_1)/n^2$, which is slightly smaller than the actual sampling <variance> $\operatorname{Var}(a_1)/n$.
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