Problem:
The life of automobile voltage regulators has an exponential distribution with a mean life of six years. You purchase a six-year-old automobile, with a working voltage regulator and plan to own it for six years.
Required:
Question 1: What is the probability that the voltage regulator fails during your ownership?
Question 2: If your regulator fails after you own the automobile three years an it is replaced, what is the mean time until the next failure?
Note: Please show how to work it out.