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midterm - MS&E 221 Ramesh Johari Midterm Examination...

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MS&E 221 Midterm Examination Ramesh Johari February 14, 2007 Instructions 1. Take alternate seating. 2. Answer all questions in the spaces provided on these sheets. If needed, additional paper will be available at the front of the room. Answers given on any other paper will not be counted. 3. The examination begins at 1:20 pm, and ends at 2:30 pm. 4. Show your work! Partial credit will be given for correct reasoning. 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). Answer each of the following short answer questions. (10 points per question) (a) True or false: In a chain on a finite state space that has two communicating classes and a unique invariant distribution, at least one of the two classes is transient. (Justify your answer.) (b) Suppose the irreducible, aperiodic transition matrix P has a greater second largest eigen- value modulus (SLEM) than the irreducible, aperiodic transition matrix Q (both on the same finite state space). Which Markov chain converges faster to its equilibrium distribution, and why?
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