5. (10 points) The following model for learning a concept over a set of lessons identifies four states of learning: I = ignorance, E = exploratory thinking, S = superficial understanding and M = mastery. If now in state I, after one lesion you have 50% chance of still being in I and 50% chance of being in E. If now in state E, you have 25% chance of being in I, 50% in E, and 25% in S. If now in state S, you have 25% chance of being in E, 50% in S, and 25% in M. If in M. you always stay in M. (a) Write out the transition matrix for this Markov chain with the absorbing state as the first state. (b) What is the expected number of rounds until mastery is attained if cur- rently in the state of exploratory thinking