# Consider the three-state Markov process below; the number given on edge (i,j) is epi, the…

Exercise 7.11 Consider the three-state Markov process below; the number given on edge (i,j) is epi, the transition rate from i to j. Assume that the process is in steady state.
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(a) Is this process reversible? (b) Find pi, the time-average fraction of time spent in state i for each i. (c) Given that the process is in state i at time t, find the mean delay from t until the process leaves state i. (d) Find ir i, the time-average fraction of all transitions that go into state i for each i. (e) Suppose the process is in steady state at time t. Find the steady-state probability that the next state to be entered is state 1. (I) Given that the process is in state 1 at time t, find the mean delay until the process first returns to state 1. (g) Consider an arbitrary irreducible finite-state Markov process in which qii = qji for all i,j. Either show that such a process is reversible or find a counter example.