I am trying to find an example of two random variables with joint CDF: $F(x, y) = \mathcal{P} ( X\leq x, Y \leq y) = I_{(x+y\geq 1)}.$
I can say that there is one such vector because given CDF is actually a CDF i.e. it satisfies all required conditions. And there is a theorem that states that in that case a random vector with given CDF exists. Is my statement correct?
It is obvious that $X$ and $Y$ are dependent and this CDF seems so simple yet I can't think of any example.