 StatLect

# Support of a random variable

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