Suppose you have two continuous random variables [math] X, Y [/math] with a joint pdf [math] f_{X, Y} [/math]. Then

[math] \Pr\{X > Y\} = \iint\limits_{\{(x,y):x > y\}} f_{X,Y}(x,y)dxdy [/math]

[math] = \int_{-\infty}^{+\infty} \int_y^{+\infty} f_{X,Y}(x,y)dxdy [/math]

[math] = \int_{-\infty}^{+\infty} \int_{-\infty}^x f_{X,Y}(x,y)dydx [/math]