## 5.1 Poisson distribution for counts (discrete)

The Poisson distribution is a discrete distribution used for modelling counts.

Definition 1.1 (Poisson distribution) The Poisson distribution has the PMF $p_X(x) = \frac{\exp(-\mu)\mu^x}{x!}\quad\text{for x=0, 1, 2, \dots},$ for $$\mu>0$$.

A Poisson process is a process in which events occur continuously and independently at a constant average rate $$\mu$$ according to a Poisson distribution.