Consider an electrical system. This system has a critical component: without this component the system doesn't work. The item has a limited lifespan, which is exponentially distributed with parameter µ. Known that the expected value of the life of the system is equal to 1 / µ. It is very expensive to replace the item. That's why there are two copies of this item in the system. The lifetimes of the two items start to count from the beginning - it is not so, the second item will only be enabled when the first tear. The lifetimes of both items are independent of each other, and are still exponentially distributed with parameter µ. The system stops functioning as both the items are gone. (Assume that the rest of the system can not break.) We are interested in the total life of the system, we call it X.
Question: Determine the distribution function x -> P (X equal or less than x).
(Hint: Remember that the life of the entire system is equal to the maximum of the lifetimes of the two copies of the item.)