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Markov Chains - dartmouth.edu

Chapter 11 Markov IntroductionMost of our study of probability has dealt with independent trials processes. Theseprocesses are the basis of classical probability theory and much of statistics. Wehave discussed two of the principal theorems for these processes: the Law of LargeNumbers and the Central Limit have seen that when a sequence of chance experiments forms an indepen-dent trials process, the possible outcomes for each experiment are the same andoccur with the same probability. Further, knowledge of the outcomes of the pre-vious experiments does not in uence our predictions for the outcomes of the nextexperiment. The distribution for the outcomes of a single experiment is su cientto construct a tree and a tree measure for a sequence ofnexperiments, and wecan answer any probability question about these experiments by using this probability theory studies chance processes for which the knowledgeof previous outcomes in uences predictions for future experiments.

Chapter 11 Markov Chains 11.1 Introduction Most of our study of probability has dealt with independent trials processes. These processes are the basis of classical probability theory and much of statistics.

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