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Math Help - Laws of Expected Values and Variance

  1. #1
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    Laws of Expected Values and Variance

    The expected values and variances of the completion times of the activities are listed here. Determine the expected value and variance of the completion time of the project.

    activity 1 2 3 4
    expected completion time(days) 18 12 27 8
    variance 8 5 6 2

    before the problem it says e(x1 + x2 + ..xk)
    and v(x1+x2+..xk)

    do I get E by calculating the average of the completion times?
    and then plug it in the e(x1+...xk) ?where the x1s are each completion time?

    thanks for any help
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    Quote Originally Posted by xfyz View Post
    The expected values and variances of the completion times of the activities are listed here. Determine the expected value and variance of the completion time of the project.

    activity 1 2 3 4
    expected completion time(days) 18 12 27 8
    variance 8 5 6 2

    before the problem it says e(x1 + x2 + ..xk)
    and v(x1+x2+..xk)

    do I get E by calculating the average of the completion times?
    and then plug it in the e(x1+...xk) ?where the x1s are each completion time?

    thanks for any help
    It is simple to prove that the mean of the sum of random variables is the sum of their means:

    e(x1 + x2 + ..xk) = e(x1) + e(x2) + ... + e(xk)

    The variance of the sum of uncorrelated random variables is the sum of their variances:

    v(x1+x2+..xk) = v(x1) + v(x2) + .... + v(xk)
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