The Poisson Process

Abstract

Suppose that an event E may occur at any point in time and that the number of occurrences of E during disjoint time intervals are independent. As examples we might think of the arrivals of customers to a store (where E means that a customer arrives), calls to a telephone switchboard, the emission of particles from a radioactive source, and accidents at a street crossing. The common feature in all these examples, although somewhat vaguely expressed, is that very many repetitions of independent Bernoulli trials are performed and that the success probability of each such trial is very small.