Let X be a random variable with probability mass function given by p(-4) = p(4) = 1/16 and p(2) = p(-2) = 7/16. Let Y = aX+b for a certain a and b.

Part A asks: For what values of a and b does Y take values in {0,1,2,3,4}?

Now, I solved this part and got a = +/- .5 and b = 2.

However, my trouble lies in figuring out the answer to this question:

Compute the probability mass function of Y for these choices of a and b.