ps1 - MS&E 221 Problem Set 1 Ramesh Johari Due:...

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Unformatted text preview: MS&E 221 Problem Set 1 Ramesh Johari Due: January 19, 2011, 5:00 PM , in the basement of Huang Eng. Ctr. Reading. Read Sections 4.1, 4.2, 4.3, and 4.5.1 in Ross. Problem 1 (Probability review). Ross, Chapter 3, problem 45: Problem 2 (Probability review). Is it possible to find random variables X , Y , and Z such that P ( X > Y ) > 1 / 2 , P ( Y > Z ) > 1 / 2 , and P ( Z > X ) > 1 / 2 ? Problem 3. For each of the following, explain whether it is reasonable to model the given process as a Markov chain. (a) The daily closing value of the S&P 500. (b) The sequence of bids observed on a single eBay auction. (c) The times at which patients arrive to the emergency room at a hospital. Problem 4. Suppose X ,X 1 ,X 2 ,... is a sequence of i.i.d. Bernoulli random variables, with P ( X n = 0) = P ( X n = 1) = 1 / 2 . 1. For n 1 , define Y n = X n + X n- 1 . Is Y 1 ,Y 2 ,Y 3 ,... a Markov chain? Explain your answer....
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This note was uploaded on 02/03/2011 for the course MS&E 221 taught by Professor Ramesh during the Winter '11 term at Stanford.

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ps1 - MS&E 221 Problem Set 1 Ramesh Johari Due:...

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