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Poisson distribution
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The Poisson distribution describes random events, for which the probability of success per trial is very small but where the number of trials is so large that there is still a reasonable rate of success.

The formula for the Poisson distribution (which can be derived from the binomial distribution - see Comparison of distributions) is

where r is the number observed and m is the mean value.

Choose values of m to see the change in the distribution shape P(r)

Note how P(r) becomes more symmetrical as m increases (1).

variance of the Poisson distribution s2= m, standard deviation s= .

An example of a Poisson distribution is the way signals emerge from a detector monitoring radioactivity.

 

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