MultivariateStatistics`
MultivariateStatistics`

# MultinormalDistribution

As of Version 8, MultinormalDistribution is part of the built-in Wolfram Language kernel.

MultinormalDistribution[μ,Σ]

represents a multivariate normal (Gaussian) distribution with mean vector μ and covariance matrix Σ.

# Details

• To use MultinormalDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
• The probability density for vector x in a multivariate normal distribution is proportional to -(x-μ).Σ-1.(x-μ)/2.
• The mean μ can be any vector of real numbers, and Σ can be any symmetric positive definite p×p matrix with p=Length[μ].
• MultinormalDistribution can be used with such functions as Mean, CDF, and RandomReal.

# Examples

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## Basic Examples(3)

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The mean of a bivariate normal distribution with correlation ρ:

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The variances of each dimension:

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Probability density function:

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