Thread: marginal density..and other..

Hello..
Im having some difficulties in my statistics questions..

Consider the function f() given by f(x,y)=k(k−1)(y−x)^(k−2), 0<x<y<1.

-Verify that if k ≥ 2 is an integer, f() is a bivariate density.
-Find the marginal densities of X and Y .
-Find E(X|Y ).
-Find E(X^2|Y = y) and V ar(X|Y ).

...it will be great if you help me at least one question.. : )...

Thank you!!

You need to integrate to find k.
I prefer 0's in my bounds so I'll integrate first wrt x



then

and

Thank you!!