Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1,

Question:

Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1, 2, and 3 is rolled. Let Y equal the outcome when a fair four-sided die that has its faces numbered 0, 4, 8, and 12 is rolled.
(a) Define the mgf of X.
(b) Define the mgf of Y.
(c) Let W = X + Y, the sum when the pair of dice is rolled. Find the mgf of W.
(d) Give the pmf of W; that is, determine P(W = w), w = 0,1, . . . ,15, from the mgf of W.