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The state of a process changes daily according to a two-state Markov chain. If the process...

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 Pi, j , where

P0,0 = 0.3, P0,1 = 0.7, P1,0 = 0.2, P1,1 = 0.8

Every day a message is sent. If the state of the Markov chain that day is i then the message sent is “good” with probability pi and is “bad” with probability qi = 1 − pi , i = 0, 1

(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?

Math   Statistics-And-Probability   
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