5. Components in a machine fail and are replaced according to a Poisson process of rate 4 a month. a) What is the expected time until 8th component fail and replaced? b) What is the probability that no component fails and replaced for 2 months? c) What is the probability that the elapsed time between the 7th and 8th replacement exceed 3 months? d) Find the probability that exactly 4 fail in the first month and exactly 8 fail in the first two months. e) Find the probability that at least 2 fail in the first month and at least 4 fail in the first two months.