A component is known to have an exponential time-to-failure distribution with a mean life of 10,000 hours.
(a) What is the probability of the component lasting at least 8000 hours?
(b) If the component is in operation at 9000 hours, what is the probability that it will last another 6000 hours?
(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 hours? Assume that the components operate independently.