Poisson Distribution

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given that the events occur independently of one another and at a known constant average rate. It is named after the French mathematician Simeon Denis Poisson, who introduced it in 1837, and it is characterized by a single parameter, usually written as lambda, equal to the average number of events expected in the interval, with both the mean and the variance of the distribution equal to that same value. The Poisson distribution is widely used to model rare, discrete events such as the number of phone calls received by a call center in an hour, the number of radioactive decays in a fixed period, or the number of mutations in a stretch of DNA, and it arises as a limiting case of the binomial distribution when the number of trials is large and the probability of success in each trial is small.