Probability Theory And Statistical Applications
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| Author | : Peter Zörnig |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 333 |
| Release | : 2016-07-11 |
| Genre | : Mathematics |
| ISBN | : 3110402831 |
This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences, in particular to readers who need or want to learn by self-study. The author is convinced that sophisticated examples are more useful for the student than a lengthy formalism treating the greatest possible generality. Contents: Mathematics revision Introduction to probability Finite sample spaces Conditional probability and independence One-dimensional random variables Functions of random variables Bi-dimensional random variables Characteristics of random variables Discrete probability models Continuous probability models Generating functions in probability Sums of many random variables Samples and sampling distributions Estimation of parameters Hypothesis tests
| Author | : Géza Schay |
| Publisher | : Birkhäuser |
| Total Pages | : 389 |
| Release | : 2016-06-17 |
| Genre | : Mathematics |
| ISBN | : 3319306200 |
Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises“/p> Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. ... the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ ... Each new concept is clearly explained and is followed by many detailed examples. ... numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)
| Author | : Rinaldo B. Schinazi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 349 |
| Release | : 2011-12-15 |
| Genre | : Mathematics |
| ISBN | : 081768249X |
This second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability. The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.
| Author | : Henry C. Tuckwell |
| Publisher | : Routledge |
| Total Pages | : 324 |
| Release | : 2018-02-06 |
| Genre | : Mathematics |
| ISBN | : 1351452959 |
This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
| Author | : James H. Stapleton |
| Publisher | : John Wiley & Sons |
| Total Pages | : 466 |
| Release | : 2007-12-14 |
| Genre | : Mathematics |
| ISBN | : 0470183403 |
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.
| Author | : Narayanaswamy Balakrishnan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 548 |
| Release | : 2021-11-24 |
| Genre | : Mathematics |
| ISBN | : 1118548558 |
INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.
| Author | : John J. Kinney |
| Publisher | : John Wiley & Sons |
| Total Pages | : 480 |
| Release | : 2015-01-13 |
| Genre | : Mathematics |
| ISBN | : 111894710X |
Praise for the First Edition "This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory." - The Statistician Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs. The Second Edition features interesting and practical examples from a variety of engineering and scientific fields, as well as: Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase Chapter-by-chapter projects that aid in the visualization of probability distributions New coverage of statistical quality control and quality production An appendix dedicated to the use of Mathematica® and a companion website containing the referenced data sets Featuring a practical and real-world approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. Probability: An Introduction with Statistical Applications, Second Edition is also an excellent reference for researchers and professionals in any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data.
| Author | : Paul L. Meyer |
| Publisher | : Oxford and IBH Publishing |
| Total Pages | : 388 |
| Release | : 1965 |
| Genre | : Mathematical statistics |
| ISBN | : |
Introduction to probability; Finite sample spaces; Conditional probability and independence; One-dimensional random variables; Functions of random variables; Two-and higher dimensional random variables; Further characterization of random variables; The poisson and other discrete random variables; Some important continuous variables; The moment-generating function; Application to reliability theory; Sums of random variables; Samples and sampling distributions; Estimation of parameters; Testing hypothesis.
| Author | : Yemima Ben-Menahem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 325 |
| Release | : 2012-01-25 |
| Genre | : Science |
| ISBN | : 3642213286 |
What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
| Author | : A. A. Sveshnikov |
| Publisher | : Courier Corporation |
| Total Pages | : 516 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486137562 |
Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.
