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3 October, 10:21

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

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  1. 3 October, 10:30
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    (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}
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