Question

A fair four sided die has two faes numbered 0 and two faces numbered 2. Another fair four sided die has its faces numbered 0,1,4, and 5. The two dice are rolled. Let X and Y be the respective outcomes of the roll. Let W = X + Y.

(a) Determine the pmf of W.

(b) Draw a probability histogram of the pmf of W

Answer 1

Answer:

Given Data,

A fair four sided die has two faces numbered 0 and two faces numbered 2. Another fair four sided die has its faces numbered 0,1,4, and 5.

The two dice are rolled. Let X and Y be the respective outcomes of the roll. Let W = X + Y.

The sample space will consist of X,Y{00,01,04,05,20,21,24,25}

Thus the sample space of W which is the sum of X and Y will consist of {0,1,2,3,4,5,6,7}

Thus the pmf will be,

X	P(X)
0	1/8
1	1/8
2	1/8
3	1/8
4	1/8
5	1/8
6	1/8
7	1/8