= Overdispersion of nondegenerate mixed Poisson counts
{title2=$\operatorname{Var}N=\mathbb EL+\operatorname{Var}L$}
If $N\mid L$ has Poisson mean $L$, <conditional expectation> and the <law of total variance> give the display. A positive <variance> of the random mean prevents the unconditional count from being Poisson. For Poisson parents of density $\lambda$ and offspring mean $\mu$, the count in $A$ has excess <variance> $\lambda\mu^2\int\kappa(A-z)^2dz$, which is positive for a bounded positive-area set and a nontrivial model.
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