Surfstat.australia: an online text in introductory Statistics

VARIATION AND PROBABILITY

DISCRETE DISTRIBUTIONS

The Poisson distribution

(work in progress)

The Poisson distribution is useful for modelling data in the form of counts: that is, non-negative integers.

The probability mass function for the Poisson distribution with parameter µ is

Pr{X=x} = exp(-µ) µx / x!, x>=0;

Since 0! is defined to be 1, the probability that X is zero is simply exp(-µ).

The mean and variance of the Poisson(µ) distribution are both equal to µ. For large µ (say, above about 10) the Poisson(µ) distribution can be reasonably well approximated by the normal(µ, µ) distribution. The continuity correction should be used.

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