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This Demonstration shows a parameterization of a bivariate normal distribution by specifying an angle of cross-correlation

. The controls

and

are the

and

spreads of the blob.

A bivariate normal distribution can be represented by three polar variables:

or with the parameters

, where

Conversely, define:

Then this gives

from

See the Wikipedia article Gaussian function.

Contributed by: Robert L. Brown

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Intuitive Parameterization of the Bivariate Normal Distribution