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Math Help - How can i calculate this

  1. #1
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    How can i calculate this

    Hi guys!!!

    A is white noise consisting of independent variables identically distributed Gaussian centered with variance = 1
    how to calculate E(A)4 ???? E(.) is the Esperance
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  2. #2
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    Re: How can i calculate this

    It's not clear what you mean. By "Esperance" you mean "exected value"? Of course, then "E^4(A)" is not just that number to the fourth power. It is, rather the "4th moment", the integral of x^4 times the probability distribution, \int_{-\infty}^\infty x^4e^{-x^2}dx. By symmetry, that is 2\int_0^\infty x^4e^{-x^2}dx.
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  3. #3
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    Re: How can i calculate this

    thnks
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: How can i calculate this

    For a standard normal distribution X, we have:

    E(X^4) = {1 \over \sqrt{2\pi}}\int_{-\infty}^\infty x^4 e^{-\frac 1 2 x^2}dx = 3

    as you can see here: Wolfram|Alpha Results

    Note that the standard normal distribution has probability density {1 \over \sqrt{2\pi}}e^{-\frac 1 2 x^2}.
    Last edited by ILikeSerena; December 31st 2012 at 12:33 PM.
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