Introduction to Probability

This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject.

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Author: Dimitri P. Bertsekas

Publisher: Athena Scientific

ISBN: 9781886529236

Category: Mathematics

Page: 544

View: 221

An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

Introduction to Probability Second Edition

The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC).

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Author: Joseph K. Blitzstein

Publisher: CRC Press

ISBN: 9780429766749

Category: Mathematics

Page: 620

View: 862

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. The second edition adds many new examples, exercises, and explanations, to deepen understanding of the ideas, clarify subtle concepts, and respond to feedback from many students and readers. New supplementary online resources have been developed, including animations and interactive visualizations, and the book has been updated to dovetail with these resources. Supplementary material is available on Joseph Blitzstein’s website www. stat110.net. The supplements include: Solutions to selected exercises Additional practice problems Handouts including review material and sample exams Animations and interactive visualizations created in connection with the edX online version of Stat 110. Links to lecture videos available on ITunes U and YouTube There is also a complete instructor's solutions manual available to instructors who require the book for a course.

A Concise Handbook of Mathematics Physics and Engineering Sciences

Bertsekas, D. P. and Tsitsiklis, J. N., Introduction to Probability, Athena Scientific, Belmont, Massachusetts, 2002. Burlington, R. S. and May, D., Handbook of Probability and Statistics With Tables, 2nd Edition, McGraw-Hill, New York, ...

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Author: Andrei D. Polyanin

Publisher: CRC Press

ISBN: 1439806403

Category: Mathematics

Page: 1125

View: 866

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students

Ruin Probabilities

P. Embrechts & N. Veraverbeke (1982) Estimates for the probability of ruin with special emphasis on the possibility of large claims. ... W. Feller (1971) An Introduction to Probability Theory and its Applications II (2nd ed.). Wiley.

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Author:

Publisher:

ISBN: 9789814466929

Category:

Page:

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Problems in Probability

Mitra, A., Quality Control and Improvement, Second Edition, Upper Saddle River: Prentice-Hall, 1998. 45.Moran, P., An Introduction to Probability Theory, Oxford: OUP, 1968. 46.Moran, P.A.P., Calculation of the normal distribution ...

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Author: T M Mills

Publisher: World Scientific Publishing Company

ISBN: 9789814551472

Category: Mathematics

Page: 192

View: 460

This is a book of problems in probability and their solutions. The work has been written for undergraduate students who have a background in calculus and wish to study probability. Probability theory is a key part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics in general — including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). Every student majoring in mathematics at university ought to take a course on probability or mathematical statistics. Probability is now a standard part of high school mathematics, and teachers ought to be well versed and confident in the subject. Problem solving is important in mathematics. This book combines problem solving and probability.

Advanced Probability Theory Second Edition

2. Show that for independent and identically distributed lognormal variables X and Y , X Y and X / Y are independent . ... An Introduction to Probability Theory and Its Applications , 2nd ed . Wiley , New York . Galambos , J. ( 1984 ) .

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Author: Janos Galambos

Publisher: CRC Press

ISBN: 0824793323

Category: Mathematics

Page: 480

View: 483

This work thoroughly covers the concepts and main results of probability theory, from its fundamental principles to advanced applications. This edition provides examples early in the text of practical problems such as the safety of a piece of engineering equipment or the inevitability of wrong conclusions in seemingly accurate medical tests for AIDS and cancer.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

Inequalities in Analysis and Probability

Erdös, P. and Kac, M. (1947). On the number of positive sums of independent random variables, Bull. Amer. Math. Soc. 53, pp. 1011–1020. Feller, W. (1966). An Introduction to Probability Theory and its Applications, Vol. 2 (second ed.) ...

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Author: Odile Pons

Publisher: World Scientific

ISBN: 9789813144002

Category: Mathematics

Page: 308

View: 647

The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

Introduction to Probability and Mathematical Statistics

The Second Edition of INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS focuses on developing the skills to build probability (stochastic) models.

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Author: Lee J. Bain

Publisher: Duxbury Press

ISBN: 0534380204

Category: Mathematics

Page: 644

View: 510

The Second Edition of INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS focuses on developing the skills to build probability (stochastic) models. Lee J. Bain and Max Engelhardt focus on the mathematical development of the subject, with examples and exercises oriented toward applications.

Probability and Statistics by Example

Nuclear Instruments and Methods in Physics Research, Series A, 572 (2007), 2, 804–807. R.L. Scheaffer. Introduction to Probability and Its Applications. 2nd ed. Belmont, CA and London: Duxbury, 1995. R.B. Schinazi.

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Author: Yuri Suhov

Publisher: Cambridge University Press

ISBN: 9781107603585

Category: Mathematics

Page: 470

View: 99

A valuable resource for students and teachers alike, this second edition contains more than 200 worked examples and exam questions.