(Semi-Markov continuation of Exercise 7.5) a) Assume that the Markov process in Exercise 7.5 is changed in the following way: whenever the process enters state 0, the time spent before leaving state 0...

(Semi-Markov continuation of Exercise 7.5) a) Assume that the Markov process in Exercise 7.5 is changed in the following way: whenever the process enters state 0, the time spent before leaving state 0 is now a uniformly distributed rv, taking values from 0 to 2/. All other transitions remain the same. For this new process, determine whether the successive epochs of entry to state 0 form renewal epochs, whether the successive epochs of exit from state 0 form renewal epochs, and whether the successive entries to any other given state i form renewal epochs.

a) For each i, find both the time-average interval and the time-average number of overall state transitions between successive visits to i.

b) Is this modified process a Markov process in the sense that Pr{X(t) = i | X(⌧ ) = j, X(s) = k} = Pr{X(t) = i | X(τ) = j} for all 0 <>τ <>