# Accession Number:

## AD0604222

# Title:

## A SIMPLE DERIVATION OF THE POSSION DISTRIBUTION

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1953-06-11

# Pagination or Media Count:

## 4.0

# Abstract:

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.

# Subject Categories:

- Operations Research