Question: . Lifetime of a component device is exponentially distributed random variable X with the rate . The probability that X is greater than 8 years

. Lifetime of a component device is exponentially distributed random variable X with the rate . The probability that X is greater than 8 years is . A system consisting of 5 such components functions correctly if all of its components function correctly. The 5 components in the system function independently. (a) Find , the expected life time and the standard deviation of a component. (b) Find the probability that a component will not fail in the next 3 years. (c) Find the probability that a component will not fail in the additional 5 years given that it didnt fail in the first 3 years. (d) Find the probability that the system will not fail in the next 3 years. (Hint) The lifetimes of the 5 components are independent, X1, X2, ..., X5; then, consider joint probability. (e) If a company purchases 5 such systems, what is the probability that exactly two will not fail in the next 3 years.

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