A
multivariate random variable or
random vector is a vector
X=(
X1,...,
Xn) whose components are
random variables on the same
probability space (Ω, P). Every such random vector gives rise to a probability measure on
Rn 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
Xi are called
marginal distributions.
Multivariate Gaussian distribution