A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees, and cordials vary from box to box. For a randomly selected box, let X and Y represent the weights of the creams and the toffees, respectively, and suppose that the joint density function of these variables is f(x, y) = 24xy, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, x+ y ≤ 1, 0, elsewhere. (a) Find the probability that in a given box the cordials account for more than 1/2 of the weight.
In letter a, it means x+y < 1/2, now how can we find the limits of the double integral? proper approach to solve this problem? thanks
PS: there would be no problem if the limits can be easily deciphered. but for this one its asking P(X + Y < 1/2)