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Question 2 (60 points) The two main Turkish telecom operators Turkcell and Vodafone are concerned about the competition of mobile subscription in the Turkey market due to new services provided by the third operator Aycell. Turkcell, the leading operator, views its survival upon recapturing market share it lost to other operators over last 10 years. To determine its present market share a survey of 1,000 mobile subscribers were conducted: 400 respondents owned a Turkcell subscription, 300 respondents owned a Vodafone subscription, and the remaining 300 respondents owned Aycell. The results of the survey is summarized below: 224 of present Turkcell subscribes said they would probably stay with Turkcell after their contract expires, 100 of them said that they would move to Vodafone, and the remaining said they would subscribe to Aycell for their next contract. 172 of present Vodafone subscribes said they would probably keep Vodafone for their next contract, 80 of them said that they would move to Turkcell, and the remaining said they would subscribe to Aycell for their next contract. 250 of present Aycell subscribers said that they were very happy with Aycell, and 218 of them said they would probably continue to the current contract for their next mobile subscription. The remaining respondents were equally likely to subscribe to Turkcell or Vodafone contract. a) (10 points) Explain if we can model the above brand switching problem as a discrete-time stochastic process. b) (10 points) Define Xn and write down the state space, S. c) (10 points) Is {Xn, n=0,1,2,...} a Markov chain? Why or why not? Explain. d) (10 points) What would be the appropriate observation points (epochs) of the owners purchase behavior? Explain. e) (10 points) Prepare a table to summarize the results of the survey. f) (10 points) Write down the one-step transition probability P matrix. Write your answers on a sheet of paper, scan it and upload. NOTE: IE336 course is being used to evaluate student performance with respect to the ABET Student Outcome, which assesses a student's ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. ABET assessment process does not effect a student's grade. The following rubric shows which S0(1) performance indicator is assessed in above question: SO (1) Item in Assessment 1a An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. Identify and define complex engineering problems. Model and formulate complex engineering problems by applying principles of engineering, science, and mathematics Solve complex engineering problems by applying principles of engineering, science, and mathematics. Question 2, Parta) Question 2, Part b), c), and d) 1b 1c Question 2, Part e) and f) Maximum file size: 100MB, maximum number of files: 1 Question 2 (60 points) The two main Turkish telecom operators Turkcell and Vodafone are concerned about the competition of mobile subscription in the Turkey market due to new services provided by the third operator Aycell. Turkcell, the leading operator, views its survival upon recapturing market share it lost to other operators over last 10 years. To determine its present market share a survey of 1,000 mobile subscribers were conducted: 400 respondents owned a Turkcell subscription, 300 respondents owned a Vodafone subscription, and the remaining 300 respondents owned Aycell. The results of the survey is summarized below: 224 of present Turkcell subscribes said they would probably stay with Turkcell after their contract expires, 100 of them said that they would move to Vodafone, and the remaining said they would subscribe to Aycell for their next contract. 172 of present Vodafone subscribes said they would probably keep Vodafone for their next contract, 80 of them said that they would move to Turkcell, and the remaining said they would subscribe to Aycell for their next contract. 250 of present Aycell subscribers said that they were very happy with Aycell, and 218 of them said they would probably continue to the current contract for their next mobile subscription. The remaining respondents were equally likely to subscribe to Turkcell or Vodafone contract. a) (10 points) Explain if we can model the above brand switching problem as a discrete-time stochastic process. b) (10 points) Define Xn and write down the state space, S. c) (10 points) Is {Xn, n=0,1,2,...} a Markov chain? Why or why not? Explain. d) (10 points) What would be the appropriate observation points (epochs) of the owners purchase behavior? Explain. e) (10 points) Prepare a table to summarize the results of the survey. f) (10 points) Write down the one-step transition probability P matrix. Write your answers on a sheet of paper, scan it and upload. NOTE: IE336 course is being used to evaluate student performance with respect to the ABET Student Outcome, which assesses a student's ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. ABET assessment process does not effect a student's grade. The following rubric shows which S0(1) performance indicator is assessed in above question: SO (1) Item in Assessment 1a An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. Identify and define complex engineering problems. Model and formulate complex engineering problems by applying principles of engineering, science, and mathematics Solve complex engineering problems by applying principles of engineering, science, and mathematics. Question 2, Parta) Question 2, Part b), c), and d) 1b 1c Question 2, Part e) and f) Maximum file size: 100MB, maximum number of files: 1