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Poisson distribution

From Simple English Wikipedia, the free encyclopedia
Typical Poisson distribution

In probability and statistics, Poisson distribution is a probability distribution. It is named after Siméon Denis Poisson. It measures the probability that a certain number of events occur within a certain period of time. The events need to be unrelated to each other. They also need to occur with a known average rate, represented by the symbol (lambda).[1]

More specifically, if a random variable follows Poisson distribution with rate , then the probability of the different values of can be described as follows:[2][3]


Examples of Poisson distribution include:

  • The numbers of cars that pass on a certain road in a certain time
  • The number of telephone calls a call center receives per minute
  • The number of light bulbs that burn out (fail) in a certain amount of time
  • The number of mutations in a given stretch of DNA after a certain amount of radiation
  • The number of errors that occur in a system
  • The number of Property & Casualty insurance claims experienced in a given period of time
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  1. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-10-06.
  2. " Poisson Distribution". www.itl.nist.gov. Retrieved 2020-10-06.
  3. Weisstein, Eric W. "Poisson Distribution". mathworld.wolfram.com. Retrieved 2020-10-06.