Mr. X owes a lot of money to the mafia. If he misses three weekly payments in a row, the mafia boss will lose her patience and Mr. X will be in big trouble (after which he will have larger problems than weekly payments). Let’s say that the probability that Mr.X misses a payment is 5%. Further, at any time, there is a probability of 2% that Mr. X manages to pull off a get-rich-quick scheme and pays off his debt. Model the system as a Markov chain so that you can then evaluate the probability to pay-offthe debt for Mr. X. Write down the transition matrix, identify matrices Q and R. Calculate the matrix N
Mr. X owes a lot of money to the mafia. If he misses three weekly payments in a row, the mafia boss will lose her patience and Mr. X will be in big trouble (after which he will have larger problems than weekly payments). Let’s say that the probability that Mr.X misses a payment is 5%. Further, at any time, there is a probability of 2% that Mr. X manages to pull off a get-rich-quick scheme and pays off his debt. Model the system as a Markov chain so that you can then evaluate the probability to pay-offthe debt for Mr. X. Write down the transition matrix, identify matrices Q and R. Calculate the matrix N and find the probability that the debt is repaid. Find the expected time until payments are a non-issue one way or the other
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