Support of a random variable

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

Table of contents

Support of a discrete variable
Support of a continuous variable
Support of random vectors and random matrices
Synonyms
More details
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Support of a discrete variable

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 function [eq1] its support, denoted by , is

Support of a continuous variable

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 function [eq3] then its support is

Support of random vectors and random matrices

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.

Synonyms

The support is sometimes also called range.

More details

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

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How to cite

Please cite as:

Taboga, Marco (2021). "Support of a random variable", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/support-of-a-random-variable.