A Collection of Probabilistic Hidden-Variable Theorems and   Counterexamples
  The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the general equivalence of the existence of a hidden variable and the existence of a joint probability distribution of the observed quatities, whether finite or continuous. 
Patrick Suppes, J. Acacio de Barros, Gary Oas