Let \(y\) follow a mixture of structural zeros of probability \(p\) and a Poisson distribution with mean \(\mu\) of probability \(q=1-p\). Show that \(E(y)=q \mu\), and \(\operatorname{Var}(y)=q \mu+p q \mu^{2}\). Thus, the variance of a ZIP outcome variable is always larger than its mean, and the phenomenon of overdispersion occurs if a Poisson regression is applied to such data.