(15 points) Consider a machine that can be either up or down on a given day. If it is up at the beginning of the a day, then it will be up at the beginning of the next day with probability 0.9. If the machine is down at the beginning of a day, then it will be up the next day with probability 0.5. (a) Model the process as a Markov chain and clearly define the state space and the onestep transition probability matrix. (b) Now assume a company maintains two of these machines that are identical, and they behave independently, Let Yn be the number of machines that are up and running at the beginning of day n. Model the process {Yn} as a Markov chain and clearly define the state space and the one-step transition probability matrix