  We study functional dependencies together with two different probabilistic
dependency notions: unary marginal identity and unary marginal distribution
equivalence. A unary marginal identity states that two variables x and y are
identically distributed. A unary marginal distribution equivalence states that
the multiset consisting of the marginal probabilities of all the values for
variable x is the same as the corresponding multiset for y. We present a sound
and complete axiomatization for the class of these dependencies and show that
it has Armstrong relations. The axiomatization is infinite, but we show that
there can be no finite axiomatization. The implication problem for the subclass
that contains only functional dependencies and unary marginal identities can be
simulated with functional dependencies and unary inclusion atoms, and therefore
the problem is in polynomial-time. This complexity bound also holds in the case
of the full class, which we show by constructing a polynomial-time algorithm.
