Poisson distribution is a discrete distribution, completely characterized by one parameter :
(where k! = 1 x 2 x ... x k).
Both the mean and the variance of Poisson distribution are equal to .
Poisson distribution describes the number of random events on an interval in space and time. If t is duration (or length) of the interval, and is the rate of the events (i.e. the average number of events per a unit interval), then . See also Poisson process for more precise definition of "random events".
For large enough values of the parameter , Poisson distribution is close to a normal distribution with the mean and the variance equal to .