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
Snapshots
Details
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.
Permanent Citation
"Joint Density of Trivariate Gaussian Random Variables"
http://demonstrations.wolfram.com/JointDensityOfTrivariateGaussianRandomVariables/
Wolfram Demonstrations Project
Published: March 7 2011
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