Let (X, Y) be an ordered pair of real-valued random variables. Say that (X, Y) is fair if E (Y ∣ X) = X a.s. It is shown, for example, that if X has a finite mean and the pair (X, Y) is fair, then X ...

This paper is concerned with the determination of tight lower and upper bounds on the expectation of a convex function of a random variable. The classic bounds are those of Jensen and ...