3. An airline reservation system has two computers, one on-line and one for backup. The operating computer fails after a random time and is replaced by the standby computer. There is one repair facility and repair times are exponentially distributed with mean i. Let X, denote the number of computers in operating condition at time 73. There are two types of computers 2' = {1, 2}, with different exponentially distributed times to failure. A computer is of type 1 (respectively, of type 2) with probability p (respectively, with probability 1 19), independent of the other computers. That is, the time to failure for a given computer has the probability distribution: 1 7 e'\"\"5 with prob. p F(t) = 1 (vs\"1\"t with prob. 1 p where (11 > 042. a. Let K E {1, 2} denote the type of computer in use at time 15. Show that {(Xt, Yt)|t 2 O} is a continuous time Markov chain. Describe the innitesimal generator Q. b. Find the stationary probabilities when p = 0.1 and a1 = 10 and a2 =