The 2-dimensional random variable (,) has the pdf : ,(,)= \begin{cases} \ 12(y - x)^2, & \text{if } 0 < x < y < 1; \\ 0, & \text{otherwise.} \end{cases}
We must compute E(X) and E(Y), for this I would like to compute both marginal pdf of X and Y. But I'm struggling with the range of the integrals in the formula. Should it be {0 to 1} for integral in (x) and integral in Y(y) or {0 to 1} for integral in (x) and {x to 1} for integral in Y(y), or neither of these ?
I can't understand how to use the range 0 < x < y < 1.
$f_X(x)=\int_x^{1} 12(y-x)^{2}dy$ for $0<x<1$,
$f_Y(y)=\int_0^{y} 12(y-x)^{2}dx$ for $0<y<1$.
I will let you carry out the integrations.