I have to compute CDF of random vector (X,Y) using the following probability density function
c x>=0, y>=0 and x+y<=2
f(x,y) = 0 otherwise
The solution has several cases (x>=0,y>=0, x+y<=2) (x>=2,0<=y<2), (y>=2,0<=x<2), (0<=x<2, 0<=y<2,x+y>=2). Why I should be interested to find these cases? Could someone help me to understand this exercise? thank you in advance.