Question

consider the following joint PDF of X and Y.

F(x,y)= 12x for 0<y<x<1,0<x^2<y<1

find the marginal of X and Y

Answer 1

$f_X\left( x \right) =\int_{x^2}^x{12xdy}=12x\left( x-x^2 \right) ,x\in \left[ 0,1 \right] \\f_Y\left( y \right) =\int_y^{\sqrt{y}}{12xdx}=6\left( y-y^2 \right) ,y\in \left[ 0,1 \right]$