To find P{X + Y > 3}, where X & Y are jointly distributed random variables, I set the limits of integration to 0-to-1 for dx and 3-x to 5 for dy. This seems reasonable given

0 < x < 1

1 < y < 5

Mr F says: The above correct.
Now, for another question, where I find P{X + Y < 1}, I am told the limits of integration should be from 0 to 1-x for dy and 0-to-1 for dx.

Mr F asks: For what values of x and y is the joint pdf of X and Y non-zero? If they're the same as above then Pr(X + Y < 1) is obviously zero ....
I don' see why,

wirefree