Joint probabilities of noncommuting operators and incompleteness of quantum mechanics

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.⁽¹⁾ The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond it, by a more general theory of single events, using hidden variables, for example.