A box contains four slips of paper marked 1 2 3 and 4 Two sl

A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for each of the following random variables shown below:
(a) x = sum of the two numbers
1, 2, 3, 4, 54, 5, 7, 8, 10     3, 5, 7, 9, 113, 4, 5, 6, 74, 6, 8, 10, 12

(b) y = difference between the first and second numbers
-3, -2, -1, 1, 2, 3-2, -1, 1, 2      -3, -1, 1, 3-4, -3, -2, 2, 3, 4-5, -3, -1, 1, 3, 5

(c) z = number of slips selected that show an even number
2, 40, 1, 2     0, 11, 20, 2

(d) w = number of slips selected that show a 1
0, 10     1, 221

Solution

Two samples are selected without replacement from four itmes marked as 1,2,3, and 4. The possible samples are

(1,2), (2,1) (1,3) (3,1) (1,4) (4,1) , (2,3) (3,2),(2,4),(4,2), (3,4), (4,3)

(a) x = sum of the two numbers

The possible values are : 3,4,5,6 and 7.

(b) y = difference between the first and second numbers

The possible values are -3,-2,-1,1,2, and 3

(c) z = number of slips selected that show an even number

The possible values are 0,1, and 2.

(d) w = number of slips selected that show a 1

The possible values are 0, 1