8 A certain mechanical component has a lifetime, \(T\) months, which has a negative exponential distribution with mean 2.5.
- A machine is fitted with 5 of these components which function independently.
- Find the probability that all 5 components are operating 3 months after being fitted.
- Find also the probability that exactly two components fail within one month of being fitted.
- Show that the probability that \(n\) independent components are all operating \(c\) months after being fitted is equal to the probability that a single component is operating \(n c\) months after being fitted.