A system has three possible states, 0, 1 and 2. Every hour it makes a transition to a different state, which is determined by a coin flip. For example, from state 0, it makes a transition to state 1 or state 2 with probabilities 0.5 and 0.5. a. Find the transition probability matrix. b. Find the three-step transition probability matrix. c. Find the steady-state distribution of the Markov chain.