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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- Dec 2nd 2012, 02:13 PMmezyexpected 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. - Dec 2nd 2012, 05:51 PMScopurRe: expected value in a beta dist.
Here's how i would approach this question:

$\displaystyle f(x|p,q) = \frac{1}{B(p,q)}x^{p-1}(1-x)^{q-1} $

So

$\displaystyle E[X^n]} = \frac{1}{B(p,q)} \int_0^1 x^{p-1+n}(1-x)^{q-1} dx $

$\displaystyle =\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?