The total mass is 1. Just use the finite set you are given.
How do you figure an mgf if the numbers of x are not consecutive, or don't start with zero? All the examples in my textbook and my lectures (and what I can find online) have x start at 0 and go to infinity. I can't figure out how to apply the formula to these homework problems:
p(x) = x/C for x=2, 4, 6, 8, 12,
p(x) = [(x-4)^2]*C for x=-3, -2, -1, 0, 1