Question

g Suppose that a die is rolled twice. What are the possible values that thefollowing 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:

(a) A = {1, 2, 3, 4, 5, 6}

(b) B = {1, 2, 3, 4, 5, 6}

(c) C = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(d) D = {-5, -4, -3, -2, -1, -0, 1, 2, 3, 4, 5}

Step-by-step explanation:

Assume each roll can result in the numbers 1, 2, 3, 4, 5, or 6.

(a) If both rolls result in a 1, the maximum value is 1. If either roll results in a 6, the maximum value is 6; all integers between 1 and 6 are also possible. Therefore, the possible values are:

A = {1, 2, 3, 4, 5, 6}

(b) If either roll results in a 1, the minimum value is 1. If both rolls result in a 6, the minimum value is 6; all integers between 1 and 6 are also possible. Therefore, the possible values are:

B = {1, 2, 3, 4, 5, 6}

(c) If both rolls result in a 1, the sum is 2. If both rolls results in a 6, the sum is 12; all integers between 2 and 12 are also possible. Therefore, the possible values are:

C = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(d) If the first roll results in a 1 and the second results in a 6, the result is -5. On the other hand, if the first roll results in a 6 and the second results in a 1, the result is 5; all integers between -5 and 5 are also possible. Therefore, the possible values are:

D = {-5, -4, -3, -2, -1, -0, 1, 2, 3, 4, 5}