Conceptual analogy between mass density and probability density – An almost non-technical note

Abstract

I show how multivariate integration over a physical object serves as a handy tool for a gentle introduction to multivariate probability theory with continuous variables. This exercise helps to visualise and thus link concepts that at first sight seem distant or even unrelated. The concepts and methods presented are digestible for advanced high school classes and above.

Keywords

• multivariate probability
• continuous random variable
• density
• physical space
• analogy
• dimensionality
• shape