# Poisson Probability Distribution

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

The following are few examples that can be modeled in Poisson experiment:

- The number of vehicles passing a specific point of a road.
- The number of inquiries received by RI office staff in one month.
- The number of night deliveries in a maternity hospital between 10:00 pm and 4:00 am.
- The number of roses in one square meter of open ground.
- The number of earthquakes of given intensity in the archipelago of Southeast Asia.