A delivery company employs a fleet of 4 delivery trucks. They want to model the number of trucks available at the beginning of each day as a Markov chain. A working truck breaks during the day with a probability of 0.1 , independently of other trucks. A separate repair company comes at night and will repair any broken trucks to have them ready for the next morning, but the repair company only shows up randomly on 20% of nights. The consulting firm you work for have asked you to answer the following: (a) Determine the transition probability matrix of this Markov chain. (b) If 4 trucks are available on Monday morning, what is the probability that 3 trucks are available on Wednesday morning? (c) Determine the classes of this Markov chain and their type, including the periodicity of any recurrent classes. (d) Explain why this Markov chain has a limiting distribution, and hence a unique stationary distribution