# marginal density..and other..

• August 31st 2009, 08:32 AM
eklee1310
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!!
• August 31st 2009, 10:13 AM
matheagle
You need to integrate to find k.
I prefer 0's in my bounds so I'll integrate first wrt x

$1=k(k-1)\int_0^1\int_0^y(y-x)^{k-2}dxdy$

then $f_X(x)=\int_0^yf_{XY}(x,y)dy$

and $f_Y(y)=\int_x^1f_{XY}(x,y)dx$
• August 31st 2009, 05:13 PM
eklee1310
Thank you!!