Question: 5. (6pts) A mechanical component in a certain system has a probability of failure de- scribed by a Weibull distribution. Let X be the random

5. (6pts) A mechanical component in a certain system has a probability of failure de- scribed by a Weibull distribution. Let X be the random variable that denotes time of failure after installation of the system. The probability density function for time to failure is then expressed as: fx (c; ), k) = AK-1 a. Suppose k = 1.5, A = 10.0 [years]. What is the expected time of failure, E[X]? b. What is the probability the component will survive (not fail) at least 20 years? c. What is the probability that two of these components in series will survive at least 20 years? (Assume they are identical.)

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