Multivariate normal distribution

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In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. A random vector is said to be multivariate normally distributed if every linear combination of its components has a univariate normal distribution. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value.

Contents

Notation and parametrization

The multivariate normal distribution of a k-dimensional random vector X = [X1, X2, …, Xk] can be written in the following notation:

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