As a (not very realistic) model of uni, suppose that students progress through Year 1, Year 2 and Year 3 and eventually rejoin the General Population according to the following transition diagram: 1/100 1/2 1/2 3/4 1 1/4 Y2 1/4 Y3 Gen Pop 99/100 1/4 1/4 In other words: every year, half of all students progress to the next year, or graduale if they are in year 3; one quarter of all students stay in the same year; and one quarter of all students slop studying and leave uni (this is in addition to graduation from Year 3). Also, every year 1% of the general population starts uni al Year 1. (a) Write down the transition matrix, P, for this Markov chain. (b) Find the equilibrium distribution for this Markov chain. (c) For this Markov chain, not all of the Detailed Balance Equations hold. Find one that fails to be true