Calculating Variance - Poisson process

**Zogru11** · March 24th 2011, 08:13 AM

Given an inhomogenous Poisson process with a given intensity lambda(t) we have a varaiable N_t which is the random number of events in a given interval. I want to calculate Var(N_t) but dont know how do that? E(N_t) is simple, one just integrates lambda over the desired interval.

**dwsmith** · March 24th 2011, 02:13 PM

Originally Posted by Zogru11

Given an inhomogenous Poisson process with a given intensity lambda(t) we have a varaiable N_t which is the random number of events in a given interval. I want to calculate Var(N_t) but dont know how do that? E(N_t) is simple, one just integrates lambda over the desired interval.

If you calculate the moment generating function, you could then do $\displaystyle\text{Var}=\frac{d^2M(t)}{dt^2}-\left(\frac{dM(t)}{dt}\right)^2$

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