A machine is subject to shocks arriving from two independent sources. The shocks from source 1 arrive according to a Poisson Process (PP) with rate 3 per day and those from source 2 at rate 4 per day, also forming a Poisson Process.
(a) What are the mean and variance of the total number of shocks from both the sources over an 8-hour shift.
(b) What is the probability that the rst incoming shock is from source 1?
(c) What is the probability that the machine is subject to a total of exactly two shocks in 1 hour?
(d) Assume that we have received a total of 5 shocks in 2 hours. What is the probability that there are exactly 2 shocks from source 1?