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Expected value (20M)

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How to do Q.19b?

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  • 6 年前
    最愛解答

    19 (a).

    Number of dots Probability

       1    1/6

       2    1/6

       3    1/6

       4    1/6

       5    1/6

       6    1/6

    Expected number of dots

    = (1)(1/6) + (2)(1/6) + (3)(1/6) + (4)(1/6) + (5)(1/6) + (6)(1/6)

    = (1 + 2 + 3 + 4 + 5 + 6) / 6

    = 21/6

    = 7/2

    = 3.5

    19 (b).

    For every question, the situation is:

     Point  Probability

      1   1/2

    -1/2  1/2

    For each question, the expected score

    = (1)(1/2) + (-1/2)(1/2)

    = 1/2 - 1/4

    = 1/4

    Therefore, for 100 such questions, the expected total score

    = 1/4 + 1/4 + ... + 1/4

    = 100/4

    = 25

    Remark:

    For (b), this is called a binomial distribution.

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