The Role of Geometry in Pairwise and Mutual Independence

Abstract

The concepts of pairwise and mutual independence, while fundamental to probability theory, are sometimes difficult for students to differentiate. For pairwise independent random variables uniformly distributed over their region of support, a “rectangular support”—a Cartesian product of intervals—for the joint density is a necessary and sufficient condition for mutual independence. The use of geometric illustrations will help students visualize this result and provide new insight into the difference between these two concepts.

Key Words:

• Cartesian product space
• Joint density
• Marginal density
• Support