Originally Posted by

**mathsandphysics** I'm stuck at this question, if anyone could help please.

$\displaystyle f XY(x,y) = kxy, 0 < x < 1, 0 <y < 1, 0 < x + y < 1$

Show k = 24, -- I proved this by taking the double integral and setting = 1.

Find the marginal probility density function of X and Y,

Find the pdf of U = X + Y, X + Y <= u ( 0 < u < 1)

My marginal pdf for X was $\displaystyle 12x(1-x)^2 , 0 < x < 1$

and for Y, was $\displaystyle 12y(1-y)^2 , 0 < y < 1$

Is this correct, and if so how would I find U = X + Y, do I integrate $\displaystyle (x+y)*24xy$

Also my epected value for E(X) and E(Y) was = 1/5