given the initial joint probability, this question is asking for the P(X>Y).

I generally know how to do these, but I am asking for an explanation/more clear description as to how you integrate the "x=y" parameter in the third step of this solution. Any explanation or help would be greatly appreciated, thank you.

(b) The probability of the event X > Y requires us to integrate the x coordinate from y to co for each y. OO e 2x - e - 20 te y/2 P{ X > Y} = dx dy 4 OO 00 3 e 3x - 2 te-2de y da dy 4 OO 1 -320 - - 2ac - - y dy = - e - e 0 4 x=y = e 1 -79/2 + -e -3y dx 4 2 0 1 e-3y = -Ty/2 _ 14 6 0 1 = + OH = 0.2381 14