We analyze the origin of quantum randomness within the.framework of a
completely deterministic theory of particle motion-Bohmian mechanics.
We show that a universe governed by this mechanics evolves in such a w
ay as to give rise to the appearance of randomness, with empirical dis
tributions in agreement with the predictions of the quantum,formalism.
Crucial ingredients in our analysis are the concept of the effective
wave function of a subsystem and that of a random system. The latter i
s a notion of interest in its own right and is relevant to any discuss
ion of the role of probability in a deterministic universe.