The life of automobile voltage regulators has an exponential

The life of automobile voltage regulators has an exponential distribution with a mean life of six years. You purchase an automobile that is six years old, with a working voltage regulator and plan to own it for six years.

a) What is the probability that the voltage regulator fails during your ownership? (Round the answer to 3 decimal places.)

b) If your regulator fails after you own the automobile three years and it is replaced, what is the mean time until the next failure?   (years)

Solution

p(t)= ?e^-?t = e^-t/6/6 (?=1/6)

a) P(T<6) = 1-e^-t/6= 1-e^-1= 0.632

b) Exponential function is memoryless function so it will remain same as mean life = 6years