Bivariate Normal Distribution

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Multivariate normal distribution
MVN redirects here. For the airport with that IATA code in Mount Vernon, Kentucky, see Mount Vernon Airport. In probability theory and statistics, a multivariate normal distribution, also sometimes called a multivariate Gaussian distribution, is a specific probability distribution, which can be thought of as a generalization to higher dimensions of the one-dimensional normal distribution (also called a Gaussian distribution). It is also closely related to matrix normal distribution.
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Bivariate Normal Distribution
Two variables follow the bivariate normal distribution if for each value of one variable, the corresponding values of another variable are normally distributed . The bivariate normal probability distribution function for a pair of continuous random variables (X and Y) is given by:



where
1, 2 are the respective means of the random variables X and Y
1, 2
is the correlation coefficient of X and Y
is the base of the natural logarithm, sometimes called Euler's e (2.71...)
is the constant Pi (3.14...)

See also, Normal Distribution , Elementary Concepts (Normal Distribution) 




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bivariate normal distribution
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