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Wiley Series in Probability and Statistics Ser.: An Introduction to Probability Theory and Its Applications, Volume 1 by William Feller (1991, Hardcover, Revised edition)
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An Introduction to Probability Theory and Its Applications uniquely blends a comprehensive overview of probability theory with the real-world application of that theory. Beginning with the background and very nature of probability theory, th then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more.