Encyclopedia > Multivariate random variable

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Multivariate random variable

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.

Table of contents

Conditional expectation

Independence

Covariance

Examples

Multivariate Gaussian distribution



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