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)=eμμxx!

where x is a discrete random variable

P(x) = probability for x occurrences
μ = the mean number of occurrences