Math Help - How to solve this integral

1. How to solve this integral

Hi,

This question is part of a series of steps in trying to prove the variance of the difference of two ordered statistics. Currently, I am stuck at the following integrand:
$a\int_{0}^{1}\int_{y(_{j})}^{1}y_{(j)}(y_{(j)}-y_{(i)})^{(j-i-1)}(1-y_{(j)})^{n-j}y_{i}^{i} dy_{(i)}dy_{(j)}$

where a is just a constant.

I have tried jacobian transformations but unsuccessful.

Could any one help?
thanks.

2. Re: How to solve this integral

Originally Posted by meeksoup
Hi,

This question is part of a series of steps in trying to prove the variance of the difference of two ordered statistics. Currently, I am stuck at the following integrand:
$a\int_{0}^{1}\int_{y(_{j})}^{1}y_{(j)}(y_{(j)}-y_{(i)})^{(j-i-1)}(1-y_{(j)})^{n-j}y_{i}^{i} dy_{(i)}dy_{(j)}$

where a is just a constant.

I have tried jacobian transformations but unsuccessful.

Could any one help?
thanks.
Is there a relationship between n, i, and j?