= Exposure time for a Poisson rate at fixed fractional precision
{title2=$T=1/(\epsilon^2R)$}
For an independent count with a <Poisson distribution> of mean $RT$, the rate estimator $N/T$ has <variance> $R/T$. Its fractional <standard deviation> is $1/\sqrt{RT}$, so achieving target fractional precision $\epsilon$ requires expected count $RT=\epsilon^{-2}$ and exposure $T=1/(\epsilon^2R)$.
For independently acquired settings with rates $R_i$, the required total exposure is $\epsilon^{-2}\sum_iR_i^{-1}$. Rare settings dominate because they require the same expected count but collect it more slowly. Simultaneous acquisition is a different design, and backgrounds or correlated systematic errors require a different uncertainty calculation.
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