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{"ops":[{"insert":"1. A system is tested for faults once per hour. If there is no fault, none "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"will be detected. If there is a fault, the probability is 0.8 that it will be detected. The "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"tests are independent of one another."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"a) If there is a fault, what is the probability that it will be detected in 1 hour or less?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"b) If there is a fault, what is the probability that it will be detected in 3 hours or "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"less?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"c) What is the mean number of tests that must be conducted in order to detect a "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"fault?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"2. The number of hits on a website follows a Poisson process with a "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"rate of 3 per minute."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"a) What is the probability that more than a minute goes by without a hit?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"b) If 2 minutes have gone by without a hit, what is the probability that a hit will "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"occur in the next minute?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"}]}

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