Question: 4. A system has 7 components, and it functions if and only if at least one of its components functions. Suppose that the lifetimes of

4. A system has 7 components, and it functions if and only if at least one of its components functions. Suppose that the lifetimes of the components are independent, identically distributed exponential random variables with mean 1 year. Furthermore, suppose that currently all the components are functional.

(a) What is the probability that two years from now the system is still functional?

(b) What is the probability that two years from now the system has at least three functional components?

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