Poisson Distribution:

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 .

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