The failures of a certain device occur according to a nonhomogeneous Poisson process whose intensity function λ(t) is given by
where t is the age (in years) of the device.
(a) Calculate the probability that a five-year-old device will have exactly two failures over the next 10 years.
(b) Knowing that the device had exactly one failure in the course of the first 5 years of the 10 years considered in (a), what is the probability that this failure took place during its sixth year of use?