midterm2009

midterm2009 - MS&E 221 Ramesh Johari Midterm...

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Midterm Examination Ramesh Johari February 11, 2009 Instructions 1. Take alternate seating if possible. 2. Answer all questions in the blue books provided. If needed, additional sheets of paper will be available at the front of the room. 3. The examination begins at 11:00 am, and ends at 12:15 pm. 4. No notes, books, or calculators are allowed. 5. The exam will be scored out of 85 points. 6. Pace yourself! Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
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Problem 1 (40 points). (Short answer) Answer each of the following questions. (a) (10 points) Suppose { X n } is a Markov chain with transition matrix P . Further, suppose that state i leads to state j , but that state j does not lead to state i . True or false : State j must be transient. If true, explain why; if false, provide a counterexample. (b) (10 points) Suppose { X n } and { Y n } are independent Markov chains. Consider a new random process
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midterm2009 - MS&E 221 Ramesh Johari Midterm...

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