# Project #45378 - assignment-1

please do give me detailed explanations and solution for all problems present in document. below are the problems.

1.    A machine is inspected at the end of every hour. It is found to be either working or failed.  If the machine is found to be working, the probability of its remaining up for the next hour is 0.90.  If is found to be failed, the machine is repaired which may take more than one hour.  Whenever the machine is failed (regardless of how long it has been down), the probability of its still being down one hour later is 0.35.

Part A:  Construct a one-step transition matrix for this Markov chain.

Part B:  Determine the mean first passage time from state i to j for all i and j.

Part C:  What is the mean number of hours until the first failure if it is currently working?

Part A:  Construct a one-step transition matrix for each of the following advertising strategies: (i) never advertise, (ii) always advertise, and (iii) follow the marketing manager's proposal.

Part B:  Determine the steady-state probabilities for each of the three cases in part A

Part C:  Find the long-run expected average profit (including a deduction for advertising costs) per quarter for each of the three advertising strategies in part A.

Part D:  Which of these strategies is best according to this measure of performance?

Part E: Given the handbag company example in question 2, list and explain two specific conditions that are possible that could cause the Markov assumption to be invalid for that model.

Part F: Given the handbag company example in question 2, list and explain two specific conditions that are possible that could cause the stationary assumption to be invalid for that model.

3.    Given the following one-step transition matrix of a Markov chain, determine:

Part A:  The classes of the Markov chain.

Part B: Indicate whether they are recurrent.

 1/4 3/4 0 0 0 3/4 1/4 0 0 0 1/3 1/3 1/3 0 0 0 0 0 3/4 1/4 0 0 0 1/4 3/4

Transition diagram that identifies the classes and transient/recurrent status.

 Subject Mathematics Due By (Pacific Time) 10/30/2014 12:00 am
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