A SIMPLE DERIVATION OF THE POSSION DISTRIBUTION

One of the most important stochastic processes is the Poisson process, in which it is assumed that a the numbers of events occurring in nonoverlapping time intervals are independent b the probability of one events occurring during time dt is lambda dt odt, where lambda is a constant, while the probability that two or more occur is odt. Using only the simplest kind of reasoning from probability theory, the Poisson distribution is deduced from the basic assumptions a and b. Consequently, the need for viewing the Poisson distribution as a limiting case of some other distribution is obviated. In addition the technique used readily generalizes to the case in which lambda depends on t.