Poisson approximation

The Poisson approximation is a method used in probability theory to approximate the binomial distribution. This approximation is useful when dealing with a large number of independent trials (n) where the probability of success (p) on each trial is very small. In such cases, the expected number of successes (n p) remains a fixed, moderate number, often denoted by (\mu).

This approximation is particularly relevant in scenarios like radioactive decay, where a large number of atoms decay over time. The Poisson distribution, named after Siméon-Denis Poisson, describes the probability of a given number of events occurring in a fixed interval of time or space. The mean and variance of the Poisson distribution are both equal to (\mu). While not as central as the central limit theorem, the Poisson approximation is a fundamental concept in the study of stochastic processes.12