Archive for November, 2009

Probability and Computing: Chapter 7 Exercises

Exercise 7.12: Let X_{n} be the sum of n independent rolls of a fair dice. Show that, for any k > 2, \lim_{n \rightarrow \infty}(X_{n} \text{is divisible by k}) = \frac{1}{k}.

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An exercise about Markov Chains

Lately¬† I have stopped reading “Probability and computing”, since I found some gaps in the exposition of the text, especially at chapter 7 “Markov Chains and Random Walks”-the authors left undefined some terminologies such as absorption. Certainly this is not the text for anybody who has little background of probability and want to learn it rigorously (though it is a good introductory text for randomized algorithm). So I bought “Markov Chains” of James Norris.
Exercises in “Markov Chains” are easy (at least for the first chapter ), though there are some problems that I am not quite sure. Here is one of them:

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