Marginal Normality Does Not Imply Bivariate Normality

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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:





Contributed by: Ehsan Azhdari (March 2011)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.