Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions. Note that the point (B,C) is then chosen at random in the unit square. Find the probability that (a) B + C < 1/2. (b) BC < 1/2. (c) |B − C| < 1/2. (d) max{B,C} < 1/2. (e) min{B,C} < 1/2.
