In the green box in the attachment I have calculated the integral of the pdf of 24xy in the same manner as in the theory that leads up to 3.1 in the attachment. But I cant see any difference in that calculation that would explain that if 24xy is dependent why is not also the theory that leads up to 3.1 dependent. In the green box I would believe that $\frac{1}{2}(1-y)^2$ is $F_X(a-y)$ for a=1. I dont see any distinctions. Why is 24xy dependent while the theory up until 3.1 is independent?

The theory is taken from Ross, A first course in probability.

Tape image twice to read it.