hmwk8new - ISyE 3232 H Ayhan and J Dai Stochastic...

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ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 H. Ayhan and J. Dai Homework 8 March 8, 2011 (Due: at the start of class on Tuesday, March 15th) 1. Consider two stocks. Stock 1 always sells for $10 or $20. If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 for tomorrow. If it is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow. Stock 2 always sells for $10 or $25. If stock 2 sells today for $10 there is a .90 chance that it will sell tomorrow for $10. If it sells today for $25, there is a .85 chance that it will sell tomorrow for $25. Let X n denote the price of the 1st stock and Y n denote the price of the 2nd stock during the n th day. Assume that { X n : n 0 } and { Y n : n 0 } are discrete time Markov chains. (a) What is the transition matrix for { X n : n 0 } ? Is { X n : n 0 } irreducible? (b) What is the transition matrix for { Y n : n 0 } ? Is { Y n : n 0 } irreducible? (c) What is the stationary distribution of { X n : n 0 } ?
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