In probability theory and statistics, the Poisson distribution (pronounced ) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. (The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.)
For instance, suppose someone typically gets on the average 4 pieces of mail per day. There will be, however, a certain spread: sometimes a little more, sometimes a little less, once in a while nothing at all. Given only the average rate, for a certain period of observation (pieces of mail per day, phonecalls per hour, etc.), and assuming that the process, or mix of processes, that produce the event flow are essentially random, the Poisson distribution specifies how likely it is that the count will be 3, or 5, or 11, or any other number, during one period of observation. That is, it predicts the degree of spread around a known average rate of occurrence.
The distribution's practical usefulness has been described by the Poisson law of large numbers.
Read more about Poisson Distribution: History, Definition, Related Distributions, Occurrence, Generating Poisson-distributed Random Variables, Bivariate Poisson Distribution
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