Question

Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:(a) the maximum value to appear in the two rolls;(b) the minimum value to appear in the two rolls;(c) the sum of the two rolls;(d) the value of the first roll minus the value of the second roll.

Answer 1

Answer and explanation:

Given : Suppose that a die is rolled twice.

The sample space form is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

To find : What are the possible values that the following random variables can take on

(a) The maximum value to appear in the two rolls;

The possible values are 1; 2; 3; 4; 5; 6.

b) The minimum value to appear in the two rolls;

The possible values are 1; 2; 3; 4; 5; 6.

c) The sum of the two rolls;

The possible values are 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12.

d) The value of the first roll minus the value of the second roll.

The possible values are -5; -4; -3; -2; -1; 0; 1; 2; 3; 4; 5.