I'm trying to do the following exercise:
Let $(X,Y)$ a random vector such that the probability function $P_{(X,Y)}$ satisfies $P_{(X,Y)}(T)=\frac{1}{2}$ and $P_{(X,Y)}(S)=\frac{1}{2}$, where $T$ is the triangle of vertices $(0,0),(1,0),(1,1)$, and $S$ is the segment that joins $(1,1)$ and $(2,0)$. Obtain the joint CDF of $(X,Y)$.
I'm struggling to see how to calculate the probability of any point on the triangle or segment, so any hints on that would be appreciated.