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Math Help - Empirical Moments problem

  1. #1
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    Empirical Moments problem

    Hello again, I hope I'm not getting on peoples nerves yet with my constant question. :/

    I have the following problem:

    Given the table:
    x 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
    f 1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1
    (doesn't quite look like I table, I know)

    a.) Calculate x (with a line on top, referring to m-prime-sub-1, the first moment about the origin)

    b.) Calculate s


    I'm annoyed that I can't get this myself. I have the formula right in front of me, but I just can't seem to apply it correctly.

    m'_{{k}} \left( x \right) ={\frac {\sum _{i=1}^{k}{x_{{i}}}^{k}f_{{i}}}{n}}

    I was able to get the answer to a.) in Maple using
    X := <(seq(i, i = 1 .. 12))> :
    F := <(1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1)> :
    Moment(X, 1, weights = F)
    (= 4.43)

    Is there a function to get the sample (s)? Either way it'd be nice to know how both formulas are applied without Maple.


    Any help (again) would be appreciated.



    [edit] Also, if I have multiple questions on different (but related, Statistics) questions, is it customary or helpful for others that I post those in separate threads?
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  2. #2
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    Quote Originally Posted by BklynKid View Post
    Hello again, I hope I'm not getting on peoples nerves yet with my constant question. :/

    I have the following problem:

    Given the table:
    x 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
    f 1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1
    (doesn't quite look like I table, I know)

    a.) Calculate x (with a line on top, referring to m-prime-sub-1, the first moment about the origin)

    b.) Calculate s
    n=\sum f_i = 56

    \bar{x}=\frac{1}{n}\sum f_i ~x_i

    and by s I presume you mean the 2-nd central moment:

    s=\frac{1}{n}\sum (x_i-\bar{x})^2 f_i

    RonL
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  3. #3
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    Thanks again for the help.
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