The support of a random variable is the set of values that the random variable can take.

For discrete random variables, it is the set of all the realizations that have a strictly positive probability of being observed.

Example If a discrete random variable has probability mass functionits support, denoted by , is

For continuous random variables, it is the set of all numbers whose probability density is strictly positive.

Example If a continuous random variable has probability density functionthen its support is

The same definition applies to random vectors. If is a random vector, its support is the set of values that it can take. The concept extends in the obvious manner also to random matrices.

The support is sometimes also called **range**.

The lecture entitled Random variables explains the concept of support in more detail.

Previous entry: Statistical model

Next entry: Test statistic

Please cite as:

Taboga, Marco (2017). "Support of a random variable", Lectures on probability theory and mathematical statistics, Third edition. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/support-of-a-random-variable.

The books

Most of the learning materials found on this website are now available in a traditional textbook format.

Featured pages

- Normal distribution
- Score test
- Poisson distribution
- Permutations
- Mean square convergence
- Convergence in probability

Explore

Main sections

- Mathematical tools
- Fundamentals of probability
- Probability distributions
- Asymptotic theory
- Fundamentals of statistics
- Glossary

About

Glossary entries

- Binomial coefficient
- Null hypothesis
- Probability space
- Precision matrix
- Distribution function
- Loss function

Share