So we have P(X>Y)=P(X−Y>0)=P((X,Y)∈C)P(X>Y)=P(X−Y>0)=P((X,Y)∈C)
Where C={(x,y):x−y>0}C={(x,y):x−y>0}
But we know how to find this, as this is the same as simply evaluating f(x,y) and integrating this over the region C.
P(X>Y)=∬Cf(x,y)dxdyP(X>Y)=∬Cf(x,y)dxdy .