36. The state of a process changes daily according to a two-state Markov chain. If the process is in state i during one day, then it is in state j the following day with probability , where Every day a message is sent. If the state of the Markov chain that day is i then the message sent is “good” with probabilityI mage and is “bad” with probabilityI mage,I mage

(a) If the process is in state 0 on Monday, what is the probability that a good message is sent on Tuesday?

(b) If the process is in state 0 on Monday, what is the probability that a good message is sent on Friday?

(c) In the long run, what proportion of messages are good?

(d) Let Image equal 1 if a good message is sent on day n and let it equal 2 otherwise. Is Image a Markov chain?
If so, give its transition probability matrix. If not, briefly explain why not.