The Bivariate Normal Distribution

The bivariate normal distribution is a distribution of a pair of variables whose conditional distributions are normal and that satisfy certain other technical conditions. The density function is a generalization of the familiar bell curve and graphs in three dimensions as a sort of bell-shaped hump. The parameters (Subscript[μ, X]) and (Subscript[μ, Y]) are the means of the coordinate variables X and Y, the parameters (Subscript[σ, X]) and (Subscript[σ, Y]) are their standard deviations, and the parameter ρ is the correlation between them.

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Contributed by: Chris Boucher

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