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Math Help - expected value in a beta dist.

  1. #1
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    expected value in a beta dist.

    If X - Beta(p,q), derive E(X^n)

    I'm having a hard time with the integration on this problem. Can anyone lead me through it?

    Thanks.
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  2. #2
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    Re: expected value in a beta dist.

    Here's how i would approach this question:
     f(x|p,q) = \frac{1}{B(p,q)}x^{p-1}(1-x)^{q-1}
    So
     E[X^n]} = \frac{1}{B(p,q)} \int_0^1 x^{p-1+n}(1-x)^{q-1} dx
     =\frac{B(p+n,q)}{B(p,q)} \int_0^1 \frac{x^{p-1+n}(1-x)^{q-1}}{B(p+n,q)} dx
    Can you finish?
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