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The theory of probability /
From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Venkatesh, Santosh S., |d 1959- | |
| 245 | 1 | 4 | |a The theory of probability / |c Santosh S. Venkatesh. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2013. | ||
| 300 | |a 1 online resource (xxiv, 805 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 347 | |a data file | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |6 880-01 |a Probability spaces -- Conditional probability -- A first look at independence -- Probability sieves -- Numbers play a game of chance -- The normal law -- Probabilities on the real line -- The Bernoulli schema -- The essence of randomness -- The coda of the normal -- Distribution functions and measure -- Random variables -- Great expectations -- Variations on a theme of integration -- Laplace transforms -- The law of large numbers -- From inequalities to concentration -- Poisson approximation -- Convergence in law, selection theorems -- Normal approximation -- Appendix: Sequences, functions, spaces. | |
| 520 | 8 | |a From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications. | |
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Probabilities |x History. | |
| 650 | 2 | |a Probability | |
| 650 | 6 | |a Probabilités. | |
| 650 | 6 | |a Probabilités |x Histoire. | |
| 650 | 7 | |a probability. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Probabilities. |2 fast |0 (OCoLC)fst01077737 | |
| 655 | 7 | |a History. |2 fast |0 (OCoLC)fst01411628 | |
| 776 | 0 | 8 | |i Print version: |a Venkatesh, Santosh S. |t Theory of probability. |d Cambridge : Cambridge University Press, 2013 |z 9781107024472 |w (DLC) 2012538878 |w (OCoLC)805015647 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=498312 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g A. |t Elements -- |g I. |t Probability Spaces -- |g 1. |t From early beginnings to a model theory -- |g 2. |t Chance experiments -- |g 3. |t sample space -- |g 4. |t Sets and operations on sets -- |g 5. |t algebra of events -- |g 6. |t probability measure -- |g 7. |t Probabilities in simple cases -- |g 8. |t Generated a-algebras, Borel sets -- |g 9. |t little point set topology -- |g 10. |t Problems -- |g II. |t Conditional Probability -- |g 1. |t Chance domains with side information -- |g 2. |t Gender biasSimpson's paradox -- |g 3. |t theorem of total probability -- |g 4. |t Le probleme des rencontres, matchings -- |g 5. |t Polya's urn scheme, spread of contagion -- |g 6. |t Ehrenfest model of diffusion -- |g 7. |t Bayes's rule for events, the MAP principle -- |g 8. |t Laplace's law of succession -- |g 9. |t Back to the future, the Copernican principle -- |g 10. |t Ambiguous communication -- |g 11. |t Problems -- |g III. |t First Look at Independence -- |g 1. |t rule of products -- |g 2. |t What price intuition-- |g 3. |t application in genetics, Hardy's law -- |g 4. |t Independent trials -- |g 5. |t Independent families, Dynkin's π-λ theorem -- |g 6. |t Problems -- |g IV. |t Probability Sieves -- |g 1. |t Inclusion and exclusion -- |g 2. |t sieve of Eratosthenes -- |g 3. |t On trees and a formula of Cayley -- |g 4. |t Boole's inequality, the Borel-Cantelli lemmas -- |g 5. |t Applications in Ramsey theory -- |g 6. |t Bontferroni's inequalities, Poisson approximation -- |g 7. |t Applications in random graphs, isolation -- |g 8. |t Connectivity, from feudal states to empire -- |g 9. |t Sieves, the Lovasz local lemma -- |g 10. |t Return to Ramsey theory -- |g 11. |t Latin transversals and a conjecture of Euler -- |g 12. |t Problems -- |g V. |t Numbers Play a Game of Chance -- |g 1. |t formula of Viete -- |g 2. |t Binary digits, Rademacher functions -- |g 3. |t independence of the binary digits -- |g 4. |t link to coin tossing -- |g 5. |t binomial makes an appearance -- |g 6. |t inequality of Chebyshev -- |g 7. |t Borel discovers numbers are normal -- |g 8. |t Problems -- |g VI. |t Normal Law -- |g 1. |t One curve to rule them all -- |g 2. |t little Fourier theory I -- |g 3. |t little Fourier theory II -- |g 4. |t idea of Markov -- |g 5. |t Levy suggests a thin sandwich, de Moivre redux -- |g 6. |t local limit theorem -- |g 7. |t Large deviations -- |g 8. |t limits of wireless cohabitation -- |g 9. |t When memory fails -- |g 10. |t Problems -- |g VII. |t Probabilities on the Real Line -- |g 1. |t Arithmetic distributions -- |g 2. |t Lattice distributions -- |g 3. |t Towards the continuum -- |g 4. |t Densities in one dimension -- |g 5. |t Densities in two and more dimensions -- |g 6. |t Randomisation, regression -- |g 7. |t How well can we estimate-- |g 8. |t Galton on the heredity of height -- |g 9. |t Rotation, shear, and polar transformations -- |g 10. |t Sums and products -- |g 11. |t Problems -- |g VIII. |t Bernoulli Schema -- |g 1. |t Bernoulli trials -- |g 2. |t binomial distribution -- |g 3. |t On the efficacy of polls -- |g 4. |t simple random walk -- |g 5. |t arc sine laws, will a random walk return-- |g 6. |t Law of small numbers, the Poisson distribution -- |g 7. |t Waiting time distributions -- |g 8. |t Run lengths, quality of dyadic approximation -- |g 9. |t curious case of the tennis rankings -- |g 10. |t Population size, the hypergeometric distribution -- |g 11. |t Problems -- |g IX. |t Essence of Randomness -- |g 1. |t uniform density, a convolution formula -- |g 2. |t Spacings, a covering problem -- |g 3. |t Lord Rayleigh's random flights -- |g 4. |t M. Poincare joue a la roulette -- |g 5. |t Memoryless variables, the exponential density -- |g 6. |t Poisson ensembles -- |g 7. |t Waiting times, the Poisson process -- |g 8. |t Densities arising in queuing theory -- |g 9. |t Densities arising in fluctuation theory -- |g 10. |t Heavy-tailed densities, self-similarity -- |g 11. |t Problems -- |g X. |t Coda of the Normal -- |g 1. |t normal density -- |g 2. |t Squared normals, the chi-squared density -- |g 3. |t little linear algebra -- |g 4. |t multivariate normal -- |g 5. |t application in statistical estimation -- |g 6. |t Echoes from Venus -- |g 7. |t strange case of independence via mixing -- |g 8. |t continuous, nowhere differentiable function -- |g 9. |t Brownian motion, from phenomena to models -- |g 10. |t Haar system, a curious identity -- |g 11. |t bare hands construction -- |g 12. |t paths of Brownian motion are very kinky -- |g 13. |t Problems -- |g B. |t Foundations -- |g XI. |t Distribution Functions and Measure -- |g 1. |t Distribution functions -- |g 2. |t Measure and its completion -- |g 3. |t Lebesgue measure, countable sets -- |g 4. |t measure on a ring -- |g 5. |t Prom measure to outer measure, and back -- |g 6. |t Problems -- |g XII. |t Random Variables -- |g 1. |t Measurable maps -- |g 2. |t induced measure -- |g 3. |t Discrete distributions -- |g 4. |t Continuous distributions -- |g 5. |t Modes of convergence -- |g 6. |t Baire functions, coordinate transformations -- |g 7. |t Two and more dimensions -- |g 8. |t Independence, product measures -- |g 9. |t Do independent variables exist-- |g 10. |t Remote events are either certain or impossible -- |g 11. |t Problems -- |g XIII. |t Great Expectations -- |g 1. |t Measures of central tendency -- |g 2. |t Simple expectations -- |g 3. |t Expectations unveiled -- |g 4. |t Approximation, monotone convergence -- |g 5. |t Arabesques of additivity -- |g 6. |t Applications of additivity -- |g 7. |t expected complexity of Quicksort -- |g 8. |t Expectation in the limit, dominated convergence -- |g 9. |t Problems -- |g XIV. |t Variations on a Theme of Integration -- |g 1. |t UTILE ERIT SCRIBIT [∫] PRO OMNIA -- |g 2. |t Change of variable, moments, correlation -- |g 3. |t Inequalities via convexity -- |g 4. |t Lp-spaces -- |g 5. |t Iterated integrals, a cautionary example -- |g 6. |t volume of an n-dimensional ball -- |g 7. |t asymptotics of the gamma function -- |g 8. |t question from antiquity -- |g 9. |t How fast can we communicate-- |g 10. |t Convolution, symmetrisation -- |g 11. |t Labeyrie ponders the diameter of stars -- |g 12. |t Problems -- |g XV. |t Laplace Transforms -- |g 1. |t transform of a distribution -- |g 2. |t Extensions -- |g 3. |t renewal equation and process -- |g 4. |t Gaps in the Poisson process -- |g 5. |t Collective risk and the probability of ruin -- |g 6. |t queuing process -- |g 7. |t Ladder indices and a combinatorial digression -- |g 8. |t amazing properties of fluctuations -- |g 9. |t Polya walks the walk -- |g 10. |t Problems -- |g XVI. |t Law of Large Numbers -- |g 1. |t Chebyshev's inequality, reprise -- |g 2. |t Khinchin's law of large numbers -- |g 3. |t physicist draws inspiration from Monte Carlo -- |g 4. |t Triangles and cliques in random graphs -- |g 5. |t gem of Weierstrass -- |g 6. |t Some number-theoretic sums -- |g 7. |t dance of the primes -- |g 8. |t Fair games, the St. |
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