= Insurance exposure
{title2=$K_j\mid\Theta\sim\operatorname{Pois}(w_j\Theta)$}
<Insurance exposure> scales the opportunity for claims: $w_j$ policy-years produce expected count $w_j\Theta$ at common annual frequency $\Theta$. Conditionally <independent> <insurance exposures> add, so the total count and total <insurance exposure> are <sufficient statistics> in a <Poisson distribution> frequency model. A yearly claim average has <conditional expectation> <independent> of the number of policies, but its <conditional variance> falls with that number.
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