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 Empirical Background | 1 |
THE SAMPLE SPACE | 7 |
The Sample Space Events | 13 |
Copyright | |
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Common terms and phrases
a₁ applies arbitrary assume balls Bernoulli trials binomial coefficient binomial distribution cards cells central limit theorem chance fluctuations chapter coefficients coin combinatorial compound Poisson distribution conditional probability consider contains corresponding defined denote derived dice digits elements equally probable equation exactly example experiment Find the probability finite follows formula frequencies function genes genotypes geometric distribution given hence inequality infinite integer intuitive k₁ large numbers law of large lemma limit theorem means mutually independent n₁ normal approximation nth trial number of paths number of successes P{AH P₁ pairs pairwise independent particle path of length player Poisson distribution population possible probability distribution probability theory problem proof Prove r₁ random walk recurrent event replacement represents result S₁ sample points sample space Show statistics Stirling's formula stochastic stochastically independent Suppose tossing total number values X₁