The task says:
A dot is randomly selected inside triangle $\{(x, y) : x > 0, y > 0, x + y < 1\}$; $(X , Y)$ are coordinates to this dot. Determine the distribution function and density of that vector.
This is sketch: https://i.stack.imgur.com/7nph8.jpg
And this is the solution: https://i.stack.imgur.com/yNlNV.jpg
I don't understand the solution to this random vector problem.
I understand that is F(x , y) which is probability P(X < x, Y < y) for f(x, y) when x <= 0 or y <= 0 = 0. I also understand that F(x, y) ) = 1 when x >= 1 and y >= 1 = 1. But I don't understand any of the other solutions so any help is greatly appriciated!