(13 points) Consider an oioe that has two copy machines. Any individual machine can be either functioning or broken down. If a particular machine is functioning at the start of a day, then during the day: a with probability 2,5 it wil break down a with probability SIS it wil not break down. Whether or not a particular machine breaks down during a day is unaifected by the other machine. Any machine that beoomes broken down remains that way until it is xed by an overnight repair person, who arrives at random as described below. The repair person works only at night and not during the day. If, at the w of a day, there are m functioning machines, then there is probability m) that the repair person will visit overnight, and probability 1 m) that the repairperson will not visit overnight. The chanoe that a repair person visits on any given night depends only on the number of functioning machines at the end of the day (and on nothing else]. Suppose that f(l]) = 3X4, f(1} = 1j3, and f(2} = ID. (Said differently, if no machines are functioning at the end of a day, then the probability the repair person visits overnight is 3/4. If one machine is functioning at the end of a day, then the probability the repair person visits overnight is 1/3. If two machines are functioning at the end of a day, then the probability the repair person visits overnight is 0.) If the repair person visits overnight, then sfhe xes exactly broken machine for the start of the next day. Derive the transition matrix of a Markov chain with states I], 1, 2 corresponding to the number of functioning machines at the END of a day (before a potential overnight repair visit}. In the matrix below, use the rst row to oorrespond to state 0, the second row to state 1, and the third row to state 2. Explain your answers. There is additional room to provide explanationfderiyation on the next page. DE