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STAT_333_Assignment_3

# STAT_333_Assignment_3 - STAT 333 Assignment 3 Due Tuesday...

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STAT 333 Assignment 3 Due: Tuesday, July 27 at the beginning of class 1. Consider a discrete-time Markov Chain with state space S = {0, …, 7} and transition matrix P = 1/2 1/4 0 0 0 0 1/4 0 1/4 0 0 0 0 0 3/4 0 0 0 1/3 0 0 0 0 2/3 0 1/5 1/5 1/5 1/5 1/5 0 0 1/6 0 0 0 1/3 1/6 1/6 1/6 0 0 0 0 0 1 0 0 1/4 0 0 0 0 0 3/4 0 0 0 2/3 0 0 0 0 1/3 a. Determine the classes of this chain, which are open or closed, write P in simplified form, and find the period of each closed class. b. Find the equilibrium distribution corresponding to each closed class. Write down the general form of all stationary distributions for this chain. c. Find the absorption probabilities from each transient state into each closed class. d. Describe the long-run behaviour of the chain if X 0 = 0. Do the same if X 0 = 3. 2. NOTE: You may use mathematical software for this question, just include your output. Consider a discrete-time Markov Chain with five transient states (1, 2, 3, 4, and 5) and two recurrent states (6 and 7). The chain is equally likely to start in any of the transient P = 1/2 0 1/4 0 0 0 1/4 0 1/3 0 1/3 0 1/3 0 1/5 1/5 1/5 1/5 1/5 0 0 0 0 0 1/4 1/4 1/4 1/4 2/3 0 1/3 0 0 0 0 0 0 0 0 0 1/2 1/2 0 0 0 0 0 1/3 2/3 states. The transition matrix is

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STAT_333_Assignment_3 - STAT 333 Assignment 3 Due Tuesday...

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