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.
Requirement:
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 and it is replaced, what is the mean time until the next failure?
Note: Could someone please give me a step by step solution?