Sorry, it's just an example, I know it doesn't actually qualify as a CDF per se, I was just wondering if the idea worked... I'm try to figure out a question using the "CDF technique" where I have f(x,y), 0<x<1, 0<y<1, and I'm trying to find g(t). So I separated it into different parts:

t<=0: G(t)=P[X+Y<t]=0

t>=2: G(t)=P[X+Y<t]=1

0<t<1: G(t)=?

1<=t<2: G(t)=?

but then when I take the derivative of G(t) I'll get two functions (one from 0 to 1, one from 1 to 2) for my g(t). Any advice?

Thanks!