Question: A component in a certain system has a probability of failure described by a Weibull distribution. Let X be the random variable that denotes time

A component in a certain system has a probability of failure described 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 given by the Weibull PDF (https://en.wikipedia.org/wiki/Weibull_distribution).

a) Suppose the data can be fitted to these parameters: = 1.5, = 12.0 years.

What is the expected time of failure, []?

b) What is the probability that one of these components will survive at least 15 years?

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