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A system is tested for faults once per hour. If there is
Chapter 4, Problem 9E(choose chapter or problem)
A system is tested for faults once per hour. If there is no fault, none will be detected. If there is a fault, the probability is 0.8 that it will be detected. The tests are independent of one another.
a. If there is a fault, what is the probability that it will be detected in 3 hours or less?
b. Given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour?
c. What is the mean number of tests that must be conducted in order to detect a fault?
Questions & Answers
QUESTION:
A system is tested for faults once per hour. If there is no fault, none will be detected. If there is a fault, the probability is 0.8 that it will be detected. The tests are independent of one another.
a. If there is a fault, what is the probability that it will be detected in 3 hours or less?
b. Given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour?
c. What is the mean number of tests that must be conducted in order to detect a fault?
ANSWER:Answer:
Step 1 of 4:
Given,
A system is tested for faults once per hour. If there is no faults, none of the faults will be detected.
Then the probability of a fault is 0.8 and the tests are independent of one another.
Let X follows Geometric distribution and probability mass function of the Geometric distribution is
P(x) = p (1 - p , x = 1, 2, …..
Where, p = 0.8