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In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the onedimensional (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 realvalued random variables each of which clusters around a mean value.
Contents
Notation and parametrization
The multivariate normal distribution of a kdimensional random vector X = [X_{1}, X_{2}, …, X_{k}] can be written in the following notation:
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