3.4.6 Poisson random variable

\(N\) is number of events that occur over some period of time.

\(N\) is a Poisson random variable if

1. \(N\left ( 0\right ) =0\)
2. Independent increments
3. \(P\left ( N=n\right ) =\frac {\lambda ^{n}e^{-\lambda }}{n!}\)

Where \(\lambda \) is the average number of events that occur over the same period that we are asking for the probability of this number of events to occur. Hence remember to adjust \(\lambda \) accordingly if we are given \(\lambda \) as rate (i.e. per unit time).