Let $X$ be the lifetime of a certain electric bulb, and $Y$ the lifetime of its replacement after the failure of the first bulb. Suppose $X$ and $Y$ are independent with common exponential density function with parameter $\lambda$.
(a) Find the probability that the combined lifetime exceeds $2\lambda$.
(b) What is the probability that the replacement outlasts the original component by $\lambda$?
Any help is appreciated.