# Poisson distribution

Poisson distribution
S. D. Poisson (1781-1840), French mathematician

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the probability distribution that describes counts of events randomly distributed in time or space, such as radioactive decay or blood cell counts. The probability of observing exactly k events in a fixed time period or region is

where λ is the average density of events in a period or region of that size and e is the base of natural logarithms (2.718). The mean and variance of the distribution are both equal to λ, thus the coefficient of variation for a Poisson distribution is

(the variability of the count is inversely proportional to the square root of the average count).

Medical dictionary. 2011.

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