The Poisson distribution is a family of discrete probability distributions on the counting numbers 0, 1, 2, 3, … , typically representing the number of occurrences of some event over a given unit of time, length, area, or other continuous unit. The distributions are parameterized by their expected number of observations over a given interval, a quantity referred to as its rate or intensity and denoted as λ. One of the oldest and most commonly used families of probability distributions, the Poisson distribution, has deep mathematical connections to many other important distributions, including the binomial distribution and the normal distribution.

Historical Context and Assumptions

The Poisson distribution is attributed to the prolific 19th – century French mathematician Siméon Denis Poisson, although it was known by the probabilist ...

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