3. There are 2 cables, A and B, transmitting signals between Sydney and Melbourne. The waiting times until cable A or cable B breaks are independent, exponential distributed with mean A (hours). Suppose that as soon as a cable breaks, the repair starts immediately. The repair times for cable A and B are independent exponential distributed random variables with mean / (hours). Let X, t > 0, be the number of cables out of order at time t (starting from 7am, Monday, say). It is well known that {Xchoo is a homogeneous continuous Markov Chain with 3 states {1, 2, 3}, where 1 = Both cables function, 2 = Exactly one cable functions, 3 = Neither cable functions.(a) Let pij(h) = P(Xh = i | Xo = i) be the transition probability of the MC. Show that pay(h) satisfies the basic assumption: Pai(h) = 1 - Ajh + o(h), pij (h) = qijh to(h), forif j, where A; and qij, i / j = 1, 2, 3 are contants that are required to be found. As a consequence, find the generator @ and the corresponding jump matrix P. (b) Suppose that a new cable will be required in case that the signal transmission stops over 3 mins on average per hour. What is the maximum ratio A/ / so that a new cable is required