Question

(12 pts) Suppose that the time (in hours) that Adam spends on an untimed pratice test follows an exponential distribution with mean 1.75 hours, and the time that Ben spends on the same test follows an exponential distribution with mean 2.25 hours. Assume that their times are independent of each other. Using appropriate notation for random variables and events:

a) Determine the probability that Ben finishes in less than 2 hours. (Show your work; you may use either the pdf or cdf.)












b) Determine the probability that both Adam and Ben finish the test in less than 2 hours. State necessary assumptions/rules along your steps.













c) Determine the probability that both Adam and Ben are still working on the test after 2 hours. (Show your work, and indicate which rules you use to combine probabilities.)















d) Determine the conditional probability that Ben is still working after 3 hours, given that he is still working after 2 hours. (Explain/justify your answer.)















e) Determine the conditional probability that Ben is still working after 2 hours, given that Adam is still working after 2 hours. (Explain/justify your answer.)

Answer 1

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