Joint Density of Trivariate Gaussian Random Variables

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This Demonstration shows a 3D plot of a level surface of the probability density function for a trivariate Gaussian (normal) density with zero means. You can adjust the standard deviations (, , ) and correlation coefficients ( , ) for the random variables with the sliders.

Contributed by: John M. Shea (March 2011)
Open content licensed under CC BY-NC-SA



The contours of equal probability density are ellipsoids in three-dimensional space.

Some things to try:

1. Start with the default variances of 1 and note the effect of changing the correlation coefficients.

2. Now change the variances to values other than 1. Vary the correlation coefficients and see how the ellipsoid changes.

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