Random variable X takes values 0 1 and 2 with equal probabil

Random variable X takes values 0, 1, and 2 with equal probability. Random variable Y takes value 3 with probability ¼, and 4 with probability ¾. Find the distribution of a) Y + X b) Y - X

Solution

a)

Y+X Probability

0+3 = 3 1/3 * 1/4 = 1/12

0 + 4 = 4 1/3 * 3/4 = 1/4

1 + 3 = 4 1/3* 1/4 = 1/12

1 + 4 =5 1/3* 3/4 = 1/4

2 + 3 = 5 1/3* 1/4 = 1/12

2 + 4 =6 1/3 * 3/4 = 1/4

3 1/12

4 1/4 + 1/12 = 1/3

5 1/4 + 1/12 = 1/3

6 1/4

b)

Y-X probability

3 - 0 = 3 1/4 * 1/3 = 1/12

3 - 1 = 2 1/4 * 1/3 = 1/12

3-2 = 1 1/4 * 1/3 = 1/12

4 - 0 = 4 3/4 * 1/3 = 1/4

4 - 1 = 3   3/4 * 1/3 = 1/4

4 - 2 = 2   3/4 * 1/3 = 1/4

y-x probability

1 1/12

2 1/12+1/4 = 1/3

3 1/12+1/4 = 1/3

4 1/4