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Math Help - expected value for range

  1. #1
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    expected value for range

    I need help with the formula for expected value of the range for ordered statistics. Do you take expected value formula for max and subtract expected value for min?

    Thanks

    Fred 1956
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  2. #2
    MHF Contributor matheagle's Avatar
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    The range is the difference, hence

    R=X_{(n)}-X_{(1)}

    these order stats are not independent, but if all you want is the mean, you don't need independence.

    E(R)=E(X_{(n)})-E(X_{(1)})
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