In a factory, the failure times of machines can be modeled by a Poisson process (Ntltgo with some rate A > 0. On average, there are three failures per unit of time. (1) Find the value of A. (ii) Evaluate the following probabilities: (a) the probability that the rst failure occurs after time 2, (b) the probability that the third failure occurs before time 4, (C) the probability that at least two failures occur during the time interval [8, 9]. (iii) We denote the successive failure times by S;