1. The problem statement, all variables and given/known data (X,Y) has joint density f_X,Y ( (x,y) = (3/16)(x+2y) for 0<y<x , 0< x<2 Evaluate E(Z) where Z = (3X+4Y)/(X+2Y) 2. Relevant equations 3. The attempt at a solution Getting the marginal densities f_X (x) =(3/8)x^2 for 0<x<2 f_Y (y) = (3/2)+(3/4)y for 0<y<2 Would I find the new distribution of 3X , 4Y, and 2Y then do the ratio distribution to solve for the distribution of Z? If this is correct, is there a shorter way?