Poisson Distribution - Definition

Definition

A discrete stochastic variable X is said to have a Poisson distribution with parameter λ>0, if for k = 0, 1, 2, ... the probability mass function of X is given by:

where

  • e is the base of the natural logarithm (e = 2.71828...)
  • k! is the factorial of k.

The positive real number λ is equal to the expected value of X, but also to the variance:

The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The Poisson distribution is sometimes called a Poissonian.

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