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problem_session_1_10-11

# problem_session_1_10-11 - MS&E 221 CA Hongsong Yuan Problem...

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MS&E 221 Problem Session 1 CA: Hongsong Yuan Jan 28, 2011 Problem 1( Expected Hitting Time ) A spider and an insect are sitting on the opposite vertices of a cube. In each time period, the spider moves to one of its adjacent vertices with even probability, while the insect stays at the same vertex all the time. What is the expected time for the spider to catch the insect? Problem 2( Verifying Recurrence/Transience ) Consider a Markov chain with the following tran- sition matrix: P = 0 . 2 0 0 0 0 . 8 0 0 0 0 0 0 0 1 0 0 . 2 0 0 . 8 0 0 0 0 0 . 5 0 . 5 0 0 0 0 0 0 . 6 0 0 . 4 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1. Identify the communicating classes. 2. Identify the positive recurrent, null recurrent and transient states. 3. Identify the periodicity for each closed class. Problem 3( Find the right Markov model ) Ross, Chapter 4, Problem 46 An individual possesses r umbrellas which he employs in going from his home to office, and vice versa. If he is at home (the office) at the beginning (end) of a day and it is raining, then he will take an umbrella with him to the office (home), provided there is one to be taken. If it is not raining, then he never takes

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