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'.