Expectation of a Joint Continuous rv

[hoddo]

fx,y = 6(x-y)dydx, if 0<y<x<1

how do you find E(XY),
i know the formula...g(x,y)fxy(x,y)dydx

but i don't know what 'g(x,y)' represents and the limits to use??

 

[matt grime]

The expectation of g(X,Y) is


$$\mathbb{E}(g(X,Y)):= \int g(x,y)f(x,y)\mathrm{d}x\mathrm{d}y$$

with the integral being taken over the whole of the probability space of X and Y.

So here, g(X,Y) is XY, and the limits are given to you: 0<y<x<1.