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 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.

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