The life of automobile voltage regulators has exponential distribution with mean life of six years. You buy an automobile that is six years old, with the working voltage regulator and plan to own it for six years.
a) Determine the probability that the voltage regulator fails throughout your ownership? (Round the answer to 3 decimal places.)
b) If your regulator fails after you own automobile three years and it is replaced, determine the mean time until the next failure?