b) The packet voice model is enhanced by examining speech in mini-slots of few micro-seconds duration. On this finer timescale, it is observed that the ON periods are interrupted by mini- OFF periods. In the OFF state, the system goes to ON with probability 0.1; otherwise, the system remains OFF. In the ON state, the system goes to OFF with probability 0.1, or goes to mini-OFF with probability 0.2; otherwise, the system remains ON. In the mini-OFF state, the system goes to OFF with probability 0.1 or goes to ON with probability 0.3; otherwise, it stays in the mini- OFF state. (i)Sketch the state transition diagram of the Markov chain with states (0) OFF, (1) ON, and (2) mini-OFF. (ii) Write the transition probability matrix P. (iii) What are the communicating classes? (iv) For each communicating class, identify the nature of periodicity of the states. (v) For each communicating class, identify whether the states are transient or recurrent. (vi) Find limiting state probabilities " (12)