Question: Freddy and Jane have entered a game in which they each win between 0 and 2 dollars. If X is the amount Freddy wins, and

Freddy and Jane have entered a game in which they each win between 0 and 2 dollars. If X is the amount Freddy wins, and Y is the amount that Jane wins, they believe that the joint density of their winnings will be
fX,Y(x,y) = 1/4xy
for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2,
And fX,Y (x,y) = 0 otherwise. Find the probability that their combined winnings exceed 2, i.e., find P(X + Y > 2).

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