# Multivariate random variable

A

**multivariate random variable** or

**random vector** is a

vector **X**=(

*X*_{1},...,

*X*_{n}) whose components are

scalar-valued

random variables on the same

probability space (Ω, P). Every such random vector gives rise to a probability measure on

**R**^{n} with the

Borel algebra as underlying

sigma-algebra. This measure is also known as the

**joint distribution** of the random vector. The distributions of each of the component random variables

*X*_{i} are called

**marginal distributions**.

Multivariate Gaussian distribution