As the picture shows:

3. An airline reservation system has two computers, one on-line and one for backup. The operat- ing oomputer 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 (t) denote the number of computers in operating condition at time t. 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 1:) (respectively, with probability 1 13}, independent of the other computers. That is, the time to failure for a. given computer has the probability diStribution: 1 6'0\" with prob. p F(t) = 1 (3021 with prob. 1 - p where o; > oz. (-51) Let Y(t) E {1, 2} denote the type of computer in use at time t. Show that {XIII}, Y{t}} is a continuous time Markov chain. Describe the innitesimal generator A. (13-) Find the stationary pmbabjties when p = [1,1 and (:1 = m and 0,2 = $4