Joint Density of Trivariate Gaussian Random Variables
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.
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.