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. The standard deviations and correlation coefficient for the random variables can be adjusted by moving the sliders. Hold down the mouse button on the 3D surface plot and drag around to change the viewing perspective.

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 +1. 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 -1. Then adjust the standard deviations for the two random variables. What are the possible angles of the major axis of the ellipses you create?