# Poisson distribution

(1.5 hours to learn)

## Summary

The Poisson distribution is a discrete probability distribution for the counts of independent random events in a given time interval, e.g. babies born in a hospital in 1 month or lightening strikes in Mexico in 1 week. It is one of the most common discrete distributions used in virtually every scientific and financial field.

## Context

This concept has the prerequisites:

- random variables
- binomial distribution (The Poisson distribution is a limiting case of the binomial distribution.)

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Probability and Statistics

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 4.7, "The poisson random variable," pages 160-173

→ Mathematical Statistics and Data Analysis

An undergraduate statistics textbook.

Location:
Section 2.1.5, "The Poisson distribution," pages 42-47

→ Mathematical Methods in the Physical Sciences

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
5.4 (p 287)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Mathematical Monk: Probability Primer (2011)

Online videos on probability theory.

→ Wikipedia

→ Wolfram MathWorld

## See also

- Poisson processes are a kind of stochastic process where counts of events within a set follow a Poisson distribution.
- For large values of the scale parameter, the Poisson distribution is well approximated by a Gaussian distribution. This follows from the Central Limit Theorem .
- The Poisson distribution is a member of the exponential family .