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STAT 333 Assignment 3

# STAT 333 Assignment 3 - STAT 333 Assignment 3 Due Monday...

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STAT 333 Assignment 3 Due: Monday April 2 at the beginning of class 1. At all times, a container holds a mixture of N balls, some white and the rest black. At each step, a coin having probability p, 0 < p < 1, of landing heads is tossed. If it is heads, a ball is chosen at random from the container and replaced by a white ball; if it is tails, a ball is chosen at random from the container and replaced by a black ball. Let X n denote the number of white balls in the container after the n th coin toss. a. Is {X n } a Markov Chain? If so, explain why. b. What are its classes? What are their periods? Are they transient or recurrent? c. Compute the transition probabilities p ij . d. Let N = 2. Find the limiting proportion of time that {X n } spends in each state. e. Based on your answer in part (d) and your intuition, guess the answer for the limiting probability when N is any positive integer. f. Prove your guess in part (e) by showing that the equilibrium equations are satisfied. g.

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STAT 333 Assignment 3 - STAT 333 Assignment 3 Due Monday...

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