# exponential distribution

(40 minutes to learn)

## Summary

The exponential distribution is a continuous distribution whose PDF decays exponentially. It is most commonly used to model the waiting time until an event occurs, where that event is equally likely to happen at any point in time.

## Context

This concept has the prerequisites:

- random variables
- cumulative distribution function (The CDF is used in analyzing waiting times.)

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

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 5.5, "Exponential random variables," pages 230-236

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 5.9, "The gamma distribution," starting with "The exponential distribution," pages 298-301

→ Mathematical Statistics and Data Analysis

An undergraduate statistics textbook.

Location:
Section 2.2.1, "The exponential density," pages 50-52

## See also

- The gamma distribution is a generalization of the exponential distribution.
- The geometric distribution is a geometric analogue of the exponential distribution.
- The exponential distribution is the only memoryless continuous distribution.
- Equivalently, it is the only continuous distribution with constant failure rate .