In: Statistics and Probability
Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6 together. After rolling both dice, let X denote the number appearing on the foursided die and Y the number appearing on the six-sided die. Define W = X +Y . Assume X and Y are independent.
(a) Find the moment generating function for W.
(b) Use the moment generating function technique to find the expectation.
(c) Use the moment generating function technique to find the variance