It's kind of hard to say "independent" about any discrete population, because once you know you are sampling from a discrete population, you can look up the val

It's kind of hard to say "independent" about any discrete population, because once you know you are sampling from a discrete population, you can look up the values of one variable given the other. So you'd only find that the variables are "independent" if you're looking at a cartesian product; in literally any other situation the variables are dependent.