We determine the bivariate probability densities with specified margins and show that the Cohen-Zaparovanny class of positive phase-space density functions, with the quantum mechanical marginal distributions of position and momentum, contains all such densities.

The trace formulation of quantum mechanical expectations is derived in a classical deterministic setting by averaging over an assembly of states. Interference of probabilities is discussed and its usual Hilbert space formulation is questioned. Nevertheless, it is shown that the observable predictions of quantum statics remain unchanged in the framework developed here.

The Bell-Wigner locality argument is shown to be a special case of the nonexistence of certain state assembles with preassigned densities when there are restrictions on the allowable states.

The effect of short disturbances on nonrelativistic motion is formulated in terms of operators. Analogies with quantum mechanics are developed and some disparities noted. For the one-dimensional particle we obtain analogues of the de Broglie wave commonly associated with particle motion, Heisenberg's commutation relation, Schrödinger's equation, and the statistical interpretation. Whether these results have any bearing on quantum mechanics itself is left an open question.