The internet service provider that students use in Ann Arbor changes yearly (be- cause of poor service and high costs) according to a two-state Markov chain. If the internet service provider is in state i in one year, then it is in state j the following year with probability Pij , where P00 = 0.45, P01 = 0.55, P10 = 0.7, and P11 = 0.3. Every year, students check the internet rates for their provider. If the state of the Markov chain that year is i then the internet rates are low with probability pi, and are high with probability qi = 1 pi, i = 0, 1. (a) (15 points) In the long run, what is the proportion of years that students have an internet service provider with high rates