Calculation of expected value of 2RVs

[nikozm]

Hello, i was wondering if the following is correct:

The expected value of (a*x+b*x*y)/(c*y) given that a,b,c are positive constants and x,y are positive random variables is:

∫∫(a*x+b*x*y)/(c*y)*f_{x}(x)*f_{y}(y)dydx (where f_{z}(.) is the PDF of z).

Thank you in advance.

 

[mathman]

It is correct as long as x and y are independent.
If not you need g(x,y) as the joint density not f_x(x)f_y(y).