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Multivariate random variable

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

Table of contents
1 Conditional expectation
2 Independence
3 Covariance
4 Examples

Conditional expectation




Multivariate Gaussian distribution