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Joint Density of Bivariate Gaussian Random Variables


	This Demonstration shows a 3D plot and a plot of a bivariate Gaussian (normal) density with zero means. You can drag the sliders for the standard deviations and and correlation coefficient for the random variables.


	Contributed by: John M. Shea
	Show Initialization Code

Some things to try:

1. Start with the default variances of 1 and note the effect of changing the correlation coefficient. What are the possible angles of the major axis of the ellipses you create?

2. Now set the correlation coefficient

to a value close to

. Then adjust the standard deviations for the two random variables. What are the possible angles of the major axis of the ellipses you create?

3. Now set the correlation coefficient

to a value close to

. Then adjust the standard deviations for the two random variables. What are the possible angles of the major axis of the ellipses you create?

Correlation Coefficient (Wolfram MathWorld)

Normal Distribution (Wolfram MathWorld)

"Joint Density of Bivariate Gaussian Random Variables" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/JointDensityOfBivariateGaussianRandomVariables/

Contributed by: John M. Shea

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