Suppose that the random variable X is the time taken by a garage to service a car. These times are distributed between 0 and 10 hours with a cumulative distribution function F(x) = A + B ln(3x + 2) for 0 ? x ? 10.
(a) Find the values of A and B and sketch the cumulative distribution function. (b) What is the probability that a repair job takes longer than two hours? (c) Construct and sketch the probability density function.