Marginal Normality Does Not Imply Bivariate Normality

This Demonstration shows an example of a bivariate distribution that has standard normal margins but is not bivariate normal. So as the title says, marginal normality does not imply bivariate normality. In contrast, it is simple to show that bivariate normality implies marginal normality.
The relevant densities are:
,
,
.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.