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.
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(c) |B − C| < 1/2.
d) max{B,C} < 1/2.
e) ) min{B,C} < 1/2.
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