Consider the following Markov chain: 0.4 0.5 0.8 0.3 0.2 (a) Give the steady-state probabilities. (b) Assume the system is in the steady state. Give the probability that the rst transition moves the system from a lower-numbered to a higher-numbered state. (c) Assume the system is in the steady state. Give the probability that the rst change of state moves the system from a lower-numbered to a higher-numbered state. (Different from (b) in that we only consider transitions that change the state.)