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.
Read more about this topic: Poisson Distribution
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