An Introduction to Probabilistic Modeling
Springer-Verlag New York Inc.
978-1-4612-6996-0 (ISBN)
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.
| Reihe/Serie | Undergraduate Texts in Mathematics |
|---|---|
| Zusatzinfo | XVI, 208 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| ISBN-10 | 1-4612-6996-2 / 1461269962 |
| ISBN-13 | 978-1-4612-6996-0 / 9781461269960 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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