exam1 - Math 4740 Exam 1, Feb 23, 2009 R. Durrett 1. (16...

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Unformatted text preview: Math 4740 Exam 1, Feb 23, 2009 R. Durrett 1. (16 points) Bob eats lunch at the campus food court every week day. He either eats Chinese food, Quesadila, or Salad. His transition matrix is C Q S C . 1 . 6 . 3 Q . 4 . 1 . 5 S . 5 . 3 . 2 He had Chinese food on Monday. What are the probabilities for his three meal choices on Wednesday (two days later)? What is the probability he will again eat Chinese food on Thursday? 2. (24 points) Classify the states in the following chain as recurrent or transient. Does p N ( x,y ) converge to a limit as N ? 1 2 3 4 5 6 7 8 1 . 2 . 3 . 5 2 . 4 . 6 3 . 1 . 2 . 7 4 1 5 . 2 . 8 6 1 7 . 5 . 5 8 . 3 . 7 3. (16 points) A regional health study shows that from one year to the next 75% of the people who smoke ( S ) will continue to smoke and 25% will stop (enter state N ). 10% of those who do not smoke will start smoking while 90% of those who do not smoke will continue to be nonsmokers. (a) This year 40% of people smoke. What will the fraction be in the next year? (b) In the long run what fraction of people will besmoke....
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exam1 - Math 4740 Exam 1, Feb 23, 2009 R. Durrett 1. (16...

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