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Math Help - What IS a moment?

  1. #1
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    What IS a moment?

    Ok, I'm doing a project on the Riemann Hypothesis. And it seems that the first four moments of the zeta-function are 1,2,42, 24024.
    But nowhere have I been able to find an explanantion for what the moment of a function actually IS.
    Figured this might be a good place to ask
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  2. #2
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    Quote Originally Posted by Fintan View Post
    Ok, I'm doing a project on the Riemann Hypothesis. And it seems that the first four moments of the zeta-function are 1,2,42, 24024.
    But nowhere have I been able to find an explanantion for what the moment of a function actually IS.
    Figured this might be a good place to ask
    Moments are results of moment generating functions which have the unique properties:

    M_x(t)=E[e^{xt}]
    M(0)=1; M'(0)=\mu ; M''(0)-M'(0)^2=\sigma
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  3. #3
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    Right - so if 42 is the third moment of the function - does that mean that you just fill in 3 instead of t and you'll get 42 as the expected value of e^3x?
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  4. #4
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    Quote Originally Posted by Fintan View Post
    Right - so if 42 is the third moment of the function - does that mean that you just fill in 3 instead of t and you'll get 42 as the expected value of e^3x?
    E[X^n] = M^{(n)}(0)

    E[X^3] = M^{(3)}(0) \Rightarrow 42
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