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140122 ||| eng |
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|a 9781461210467
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| 100 |
1 |
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|a Bremaud, Pierre
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| 245 |
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|a An Introduction to Probabilistic Modeling
|h Elektronische Ressource
|c by Pierre Bremaud
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| 250 |
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|a 1st ed. 1988
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| 260 |
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|a New York, NY
|b Springer New York
|c 1988, 1988
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| 300 |
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|a XVI, 208 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Probability Theory
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| 653 |
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|a Probabilities
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a Undergraduate Texts in Mathematics
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| 028 |
5 |
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|a 10.1007/978-1-4612-1046-7
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4612-1046-7?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 519.2
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| 520 |
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|a 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
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