Wolfram Demonstrations Project

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

Rotate and Zoom in 3D

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.

Normal Distribution (Wolfram MathWorld)

Probability Density Function (Wolfram MathWorld)

Standard Deviation (Wolfram MathWorld)

"Joint Density of Trivariate Gaussian Random Variables" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/JointDensityOfTrivariateGaussianRandomVariables/

Contributed by: John M. Shea

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Joint Density of Trivariate Gaussian Random Variables

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