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.
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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.
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