[10 10] The time X (in hours) it takes auto mechanic A to

Chapter 0, Problem SE4.14

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[10 10] The time X (in hours) it takes auto mechanic A to complete a car inspection may be considered a random variable uniformly distributed on (2, 3.5). The time Y it takes auto mechanic B to do the same job is a random variable uniformly distributed on (1.5, 3.0). Assume that A and B started working on different cars at the same time and that X and Y are independent. a. Find the joint pdf of (X, Y ) and calculate the probability that both A and B finish their jobs in less than 2.5 hours. b. Find the probability that B finishes the job first.

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