Answer Happy

Problem 9 Consider the Markov chain in Fig. 7.22. Let us refer to a transition a that results in a state with a higher (respectively. lower) index as a birth respectively, death). Calculate the following quantities, assuming that when we start observing the chain. It is already in steady-state 0.4 0.5 0.8 GO 0.6 0.2 0.3 0.2 Figure 7.22: Transition probability graph for Problem 11 (a) For each state 1. the probability that the current state is 1. (b) The probability that the first transition we observe is a birth (c) The probability that the first change of state we observe is a birth (d) The conditional probability that the process was in state 2 before the first tran- sition that we observe, given that this transition was a birth. (e) The conditional probability that the process was in state 2 before the first change of state that we observe given that this change of state was a birth (f) The conditional probability that the first observed transition is a birth given that it resulted in a change of state. () The conditional probability that the first observed transition leads to state 2. given that it resulted in a change of state.