For questions relating to the index of dispersion, or the variance-to-mean ratio for a random variable or stochastic process.

Given a stochastic process, $\{N(t), t\ge0\}$, which counts the number of events by time $t$, the index of dispersion (for counts) is the variance-to-mean ratio of the cumulative number of events by time $t$.

More succinctly, $I(t) = \operatorname{Var}(N(t))/\Bbb E[N(t)]$.

For further details see Wikipedia: Index of Dispersion.