- Operations Research Stochastic Models 1 (59.71 KiB) Viewed 97 times
operations research stochastic models
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answerhappygod
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operations research stochastic models
operations research stochastic models
Question 3 (50 points) Consider the above situation in which a section of highway is inspected for damage at the end of each year. Based on specific measurements of frequency, and depths of cracks, the highway section is classified to be in one of four possible grades of deterioration: "Good as new" (1). "Minor Deterioration" (2). "Usable" (3), and "Unusable" (4). Damage is progressive and eventually the highway section becomes unusable. Once it becomes unusable, the section of the highway is repaired until the next inspection and its' grade becomes "Good as new". Past experience suggests that probability of deteriorating one grade between two inspections is 0.27, and two grades is 0.33. The highway section does not deteriorate three grades between two inspections, and it is possible that it does not deteriorate at all between two inspections. a) (20 points) Draw the transition diagram of the Discrete Time Markov Chain b) (10 points) Write down the P-matrix c) (10 points) What is the probability P(X3-3]X2-2, X1=2, X=0)? d) (10 points) Suppose you are given a realization (1,1,2,3). Explain in your own words the meaning of this realization Write your answers on a sheet of paper, scan it and upload.
Question 3 (50 points) Consider the above situation in which a section of highway is inspected for damage at the end of each year. Based on specific measurements of frequency, and depths of cracks, the highway section is classified to be in one of four possible grades of deterioration: "Good as new" (1). "Minor Deterioration" (2). "Usable" (3), and "Unusable" (4). Damage is progressive and eventually the highway section becomes unusable. Once it becomes unusable, the section of the highway is repaired until the next inspection and its' grade becomes "Good as new". Past experience suggests that probability of deteriorating one grade between two inspections is 0.27, and two grades is 0.33. The highway section does not deteriorate three grades between two inspections, and it is possible that it does not deteriorate at all between two inspections. a) (20 points) Draw the transition diagram of the Discrete Time Markov Chain b) (10 points) Write down the P-matrix c) (10 points) What is the probability P(X3-3]X2-2, X1=2, X=0)? d) (10 points) Suppose you are given a realization (1,1,2,3). Explain in your own words the meaning of this realization Write your answers on a sheet of paper, scan it and upload.