Independence, Conditional Expectation, and Zero Covariance
Jeffrey J. Hunter · The American Statistician · 1972
In many introductory probability and statistics courses the concept,s of independent random variables, conditional random variable;, expectation and covariance are discussed when the topic of bivariate random variables is presented. The result that independence implies zero covariance and an example to show that the converse does not necessarily follow are invariably included in the course. In this note we show that by introducing conditional expectations (regression curves) at the same time we are abIe to link these concepts and present a unified approach. The author does not claim that any of the examples included in this note are original. However, it is considered that their assembly together adds to their usefulness.