Suppose that a point (X, Y) is to be chosen from the square S in the xy-plane containing all points (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Suppose that the probability that the chosen point will be the corner (0, 0) is 0.1, the probability that it will be the corner (1, 0) is 0.2, the probability that it will be the corner (0, 1) is 0.4, and the probability that it will be the corner (1, 1) is 0.1. Suppose also that if the chosen point is not one of the four corners of the square, then it will be an interior point of the square and will be chosen according to a constant p.d.f. over the interior of the square. Determine
(a) Pr(X ≤ 1/4)
(b) Pr(X + Y ≤ 1).