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Math Help - Uniform sum distribution.

  1. #1
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    Oct 2010
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    Uniform sum distribution.

    Hi,
    I have a problem with calculating sum of n uniform variables on the interval [0,1].

    I found solution here:
    Uniform Sum Distribution -- from Wolfram MathWorld
    I was thinking about charakteristic function but I do not understand one line:

    Assume we calculated characteristic function of that sum and we obtained  (\frac{i(1-e^{i t})}{t})^n.
    Then we want to calculate probability density ( using  P(x)= \frac{1}{2 \Pi} \int_{- \infty}^ {\infty} e^{- i t x } \phi(t) dt

    But I do not know how calculate:  P(x)= \frac{1}{2 \Pi} \int_{- \infty}^ {\infty} e^{- i t x } (\frac{i(1-e^{i t})}{t})^n dt

    Please give me a hint
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  2. #2
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    Apr 2012
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    Gothenburg
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    Thanks
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    Re: Uniform sum distribution.

    If the integer n is greater than 3, then you may safely invoke the Central limit theorem and claim that the exact probability distribution of the sum resembles a certain normal probability distribution; if you want to investigate the rate of convergence to the normal distribution, I suggest taking a look at the Berry-EssÚn theorem.
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