Joint density g(y1,y2,y3) = e^(-y3)*y2*y3^2
0<y1<1, 0<y2<1, 0<y3<+inf
marginal density g(y1),g(y2),g(y3) is supposed to be indepent so g(y1)*g(y2)*g(y3) = g(y1,y2,y3)
However, I keep getting wrong anwer and I do not know why?
Maybe there is some trick for setting up the boundary for integration?
I have g(y1) = 1, g(y2) = 1, g(y3) = (e^(-y3)*y3^2)/2.
What wrong with my calculation?