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An Introduction to Probabilistic Modeling / by Pierre Bremaud
(Undergraduate Texts in Mathematics. ISSN:21975604)
版 | 1st ed. 1988. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 1988 |
本文言語 | 英語 |
大きさ | XVI, 208 p : online resource |
著者標目 | *Bremaud, Pierre author SpringerLink (Online service) |
件 名 | LCSH:Probabilities FREE:Probability Theory |
一般注記 | 1 Basic Concepts and Elementary Models -- 1. The Vocabulary of Probability Theory -- 2. Events and Probability -- 3. Random Variables and Their Distributions -- 4. Conditional Probability and Independence -- 5. Solving Elementary Problems -- 6. Counting and Probability -- 7. Concrete Probability Spaces -- Illustration 1. A Simple Model in Genetics: Mendel’s Law and Hardy—Weinberg’s Theorem -- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle -- Illustration 3. Bertrand’s Paradox -- 2 Discrete Probability -- 1. Discrete Random Elements -- 2. Variance and Chebyshev’s Inequality -- 3. Generating Functions -- Illustration 4. An Introduction to Population Theory: Galton—Watson’s Branching Process -- Illustration 5. Shannon’s Source Coding Theorem: An Introduction to Information Theory -- 3 Probability Densities -- I. Expectation of Random Variables with a Density -- 2. Expectation of Functionals of Random Vectors -- 3. Independence -- 4. Random Variables That Are Not Discrete and Do Not Have a pd -- Illustration 6. Buffon’s Needle: A Problem in Random Geometry -- 4 Gauss and Poisson -- 1. Smooth Change of Variables -- 2. Gaussian Vectors -- 3. Poisson Processes -- 4. Gaussian Stochastic Processes -- Illustration 7. An Introduction to Bayesian Decision Theory: Tests of Gaussian Hypotheses -- 5 Convergences -- 1. Almost-Sure Convergence -- 2. Convergence in Law -- 3. The Hierarchy of Convergences -- Illustration 8. A Statistical Procedure: The Chi-Square Test -- Illustration 9. Introduction to Signal Theory: Filtering -- Additional Exercises -- Solutions to Additional Exercises Introduction to the basic concepts of probability theory: independence, expectation, convergence in law and almost-sure convergence. Short expositions of more advanced topics such as Markov Chains, Stochastic Processes, Bayesian Decision Theory and Information Theory HTTP:URL=https://doi.org/10.1007/978-1-4612-1046-7 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781461210467 |
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EB00227395 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000105196 |
ISBN | 9781461210467 |
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