The number of occurrences in a given time interval or in a given space can be modeled using Poisson Distribution if the following conditions are being satisfied:
- The events occur at random.
- The events are independent from one another.
- The average rate of occurrences is constant.
- There are no simultaneous occurrences.
The Poisson distribution is defined as
$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$
where x is a discrete random variable
P(x) = probability for x occurrences
μ = the mean number of occurrences