(10 points) Problem 1 a. (5 points) Suppose that on any given day, a machine can be in good condition (G), in poor condition (P), or broken (B). If the machine is in good condition on a particular day, then it remains in good condition on the next day with probability 0.7, it is in poor condition the next day with probability 0.2, and with probability 0.1 it is broken the next day. Similarly, if the machine is in poor condition on a particular day, then it remains in poor condition on the next day with probability 0.6, and it is broken on the next day with probability 0.4. Finally, with probability 0.5, it takes exactly one day to repair a broken machine; otherwise (i.e., with probability 0.5), it takes exactly two days to repair a broken machine. Show that this situation can be modeled using a Markov chain (i.e., specify your model and show it is a Markov chain), and determine the state space of this Markov chain and its transition probability matrix. Explain.