Let X and Y equal the outcomes when two fair six-sided

Problem 11E

Let X and Y equal the outcomes when two fair six-sided dice are rolled. Let W = X + Y. Assuming independence, find the pmf of W when

(a) The first die has three faces numbered 0 and three faces numbered 2, and the second die has its faces numbered 0, 1, 4, 5, 8, and 9.

(b) The faces on the first die are numbered 0, 1, 2, 3, 4, and 5, and the faces on the second die are numbered 0, 6, 12, 18, 24, and 30.

                                                       Step by Step Solution

Step 1 of 3

(a)

Given  has a six-sided die with faces 0, 0, 0,2,2,2.

 Represents a six-sided die with faces 0, 1,4,5,8 and 9.

A fair four sided has an equal chance to roll a face,

The moment generating function is,

The moment generating function is,

Let

Then,

The probability at  is, .