Answer all questions with detailed explanation

A component is known to have an exponential time-to-failure distribution with a mean life of 10,000 h.

a)What is the probability of the component lasting at least 8000 h?

b)If the component is in operation at 9000 h, what is the probability that it will last another 6000 h?

c)Two such components are put in parallel, so that the system will be in operation if at least one of the components is operational. What is the probability of the system being operational for 12,000 h? Assume that the components operate independently