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 14 at 2:30 pm (in class) You may use your favourite math software for the matrix manipulation. Just include your output. Type I Problems 1. #10, page 265 of the text, 9 th edition. 2. #11, page 265 of the text, 9 th edition. 3. #25, page 267 of the text, 9 th edition. 4. #33, page 268 of the text, 9 th edition. Type II Problems 1. Consider a sequence of repeated independent tosses of a fair coin, each toss resulting in H or T. For each n = 1, 2, 3, . . . define X n = length of the run after the n th toss where a run is a maximal sequence of like outcomes (i.e., all H or all T). For example, if the sequence of outcomes looks like H H T H H H H T … then X 1 = 1, X 2 = 2, X 3 = 1, X 4 = 1, X 5 = 2, X 6 = 3, X 7 = 4, X 8 = 1, etc. a. Model this as a Markov chain by writing down the state space S and transition matrix P . b. Prove that this chain is irreducible and find the period of the chain. c.

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STAT_333_Assignment_3 - STAT 333 Assignment 3 Due Tuesday...

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