An Introduction to Probability Theory and Its Applications, Volume 1A complete guide to the theory and practical applications of probability theory 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, the book 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. The book's comprehensive approach provides a complete view of theory along with enlightening examples along the way. |
Contents
THE NATURE OF PROBABILITY THEORY 1 The Background | 1 |
Statistical Probability | 4 |
Summary | 5 |
Copyright | |
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a₁ applies arbitrary arc sine arrangements assume balls Bernoulli trials binomial coefficient binomial distribution Bose-Einstein statistics cards cells chance fluctuations chapter coin combinatorial conditional probability consider corresponding defined denote dice digits elements equally probable event example experiment Fermi-Dirac statistics Find the probability finite follows frequencies function genes genotypes geometric distribution given hence hypergeometric distribution inequality integer intuitive k₁ large numbers law of large lemma limit theorem means mutually independent n₁ number of paths number of successes outcomes P{AH P₁ pairs pairwise independent particles path of length player Poisson distribution population positive integer possible probability distribution probability theory problem proof Prove r₁ r₂ random variables random walk represents result S₁ sample points sample space sequence Show statistics Stirling's formula stochastic stochastically independent Suppose tossing total number values X₁