# beta distribution

(55 minutes to learn)

## Summary

The beta distribution is a probability distribution over the unit interval. It is most commonly used in Bayesian statistics as the conjugate prior for the Bernoulli distribution.

## Context

This concept has the prerequisites:

- random variables
- expectation and variance
- gamma function (The gamma function is part of the normalizing constant of the beta distribution.)

## Goals

- Know the PDF of the beta distribution

- Be able to compute the expectation of a beta random variable

- Express the uniform distribution as a special case of the beta distribution

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

## -Paid-

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 5.10, "The beta distribution," pages 303-308

Additional dependencies:

- binomial distribution

Other notes:

- The proof of the identity about products of gamma functions is optional.

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

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 5.6.4, "The beta distribution," pages 240-241

## See also

- The beta distribution is the conjugate prior for the Bernoulli and binomial distributions.
- The Dirichlet distribution is a multivariate generalization of the beta distribution.