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# hw9 - EE 351K Probability Statistics and Random Processes...

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EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 9: Markov Chains Due Monday, April 27th 2009 Problem 1 A spider and a fly move along a straight line in unit increments. The spider always moves towards the fly by one unit. The fly moves towards the spider by one unit with probability 0.3, moves away from the spider with probability 0.3 and stays in place with probability 0.4. When the spider and fly land in the same position, the spider captures the fly. 1. Construct a Markov chain that describes the relative location of the spider and fly. 2. Identify the transient and recurrent states. Problem 2 A professor gives tests that are hard, medium or easy. If she gives a hard test, her next test will be either medium or easy with equal probability. However, if she gives a medium or easy test, there is a 0.5 probability that her next test will be of the same difficulty, and a 0.25 probability for each of the other two levels of difficulty. Construct an appropriate Markov chain and find the steady-state probabilities.
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• Spring '07
• BARD
• Probability theory, Stochastic process, Markov chain, Continuous-time Markov process, Andrey Markov, Random walk

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