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:

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