Multivariate random variable

A multivariate random variable or random vector is a vector X=(X₁,...,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 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 X_i are called marginal distributions.

Table of contents

1 Conditional expectation 2 Independence 3 Covariance 4 Examples

Conditional expectation

Independence

Covariance

Examples

Multivariate Gaussian distribution