The theory of probability / Santosh S. Venkatesh.

Format:

Book

Author/Creator:

Venkatesh, Santosh S., author.

Language:

English

Subjects (All):

Probabilities.

Probabilities--History.

Physical Description:

1 online resource (xxiv, 805 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

Summary:

From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful book is a fascinating reference and essential resource, for all engineers, computer scientists and mathematicians.

Contents:

Cover; THE THEORY OF PROBABILITY; Title; Copyright; Dedication; Contents; Preface; Part A: ELEMENTS; I Probability Spaces; 1 From early beginnings to a model theory; 2 Chance experiments; 3 The sample space; 4 Sets and operations on sets; 5 The algebra of events; 6 The probability measure; 7 Probabilities in simple cases; DISCRETE SPACES; CONTINUOUS SPACES; 8 Generated σ-algebras, Borel sets; 9 A little point set topology; 10 Problems; II Conditional Probability; 1 Chance domains with side information; 2 Gender bias? Simpson's paradox; 3 The theorem of total probability

4 Le problème des rencontres, matchings5 Pólya's urn scheme, spread of contagion; 6 The Ehrenfest model of diffusion; EXTENSION: BIRTH-DEATH CHAINS; 7 Bayes's rule for events, the MAP principle; 8 Laplace's law of succession; 9 Back to the future, the Copernican principle; 10 Ambiguous communication; 11 Problems; III A First Look at Independence; 1 A rule of products; 2 What price intuition?; 3 An application in genetics, Hardy's law; 4 Independent trials; 5 Independent families, Dynkin's π-λ theorem; 6 Problems; IV Probability Sieves; 1 Inclusion and exclusion; 2 The sieve of Eratosthenes

3 The independence of the binary digits4 The link to coin tossing; 5 The binomial makes an appearance; 6 An inequality of Chebyshev; 7 Borel discovers numbers are normal; 8 Problems; VI The Normal Law; 1 One curve to rule them all; 2 A little Fourier theory I; 3 A little Fourier theory II; 4 An idea of Markov; 5 Lévy suggests a thin sandwich, de Moivre redux; 6 A local limit theorem; 7 Large deviations; 8 The limits of wireless cohabitation; 9 When memory fails; 10 Problems; VII Probabilities on the Real Line; 1 Arithmetic distributions; 2 Lattice distributions; 3 Towards the continuum

4 Densities in one dimension5 Densities in two and more dimensions; 6 Randomisation, regression; 7 How well can we estimate?; 8 Galton on the heredity of height; 9 Rotation, shear, and polar transformations; 10 Sums and products; 11 Problems; VIII The Bernoulli Schema; 1 Bernoulli trials; 2 The binomial distribution; 3 On the efficacy of polls; 4 The simple random walk; 5 The arc sine laws, will a random walk return?; 6 Law of small numbers, the Poisson distribution; 7 Waiting time distributions; 8 Run lengths, quality of dyadic approximation; 9 The curious case of the tennis rankings

10 Population size, the hypergeometric distribution

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-23613-4

1-107-25461-2

1-139-85413-5

1-139-84031-2

1-139-84505-5

1-139-84269-2

1-299-40924-5

1-139-84150-5

1-139-16932-7

OCLC:

821869892