Let $X_1$ and $X_2$ be iid Random Variables. The question is to find P($X_1$<$X_2$) using transformations.
So, what I tried:
Let $Y_1=X_1-X_2\\ Y_2=X_2\\ u = x - y, v = y\\ |J| = 1\\f_{uv}=f_{xy}(u+v,v)\\P(Y_1<0,Y_2<\infty) = \int^{0}_{-\infty} \int^{\infty}_{-\infty} f_{xy}(u+v,v)$
Now, I'm stuck.