Independence and Dependence

The concepts of independent and dependent variables are basic to the study of relationships between variables. The approach used here is closely related to Tjur (1980, p. 120); however, the study of independence and dependence has a long history in statistics, as evident from De Moivre (1756) and Bayes (1763). In Section 6.1, a general definition of independent variables is provided, and some basic consequences of independence are considered. In Section 6.2, conditional expectations are used to study dependence between variables.