*An Introduction*

Author: Geoffrey Grimmett,Dominic Welsh

Publisher: OUP Oxford

ISBN: 0191019925

Category: Mathematics

Page: 288

View: 1445

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### Probability

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

### Probability

Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.

### Probability: An Introduction

Probability: An Introduction provides the fundamentals, requiring minimal algebraic skills from the student. It begins with an introduction to sets and set operations, progresses to counting techniques, and then presents probability in an axiomatic way, never losing sight of elucidating the subject through concrete examples. The book contains numerous examples and solved exercises taken from various fields, and includes computer explorations using Maple.

### Probability

Praise for the First Edition "This is a well-written and impressively presentedintroduction to probability and statistics. The text throughout ishighly readable, and the author makes liberal use of graphs anddiagrams to clarify the theory." - The Statistician Thoroughly updated, Probability: An Introduction withStatistical Applications, Second Edition features acomprehensive exploration of statistical data analysis as anapplication of probability. The new edition provides anintroduction to statistics with accessible coverage of reliability,acceptance sampling, confidence intervals, hypothesis testing, andsimple linear regression. Encouraging readers to develop a deeperintuitive understanding of probability, the author presentsillustrative geometrical presentations and arguments without theneed for rigorous mathematical proofs. The Second Edition features interesting and practicalexamples from a variety of engineering and scientific fields, aswell as: Over 880 problems at varying degrees of difficulty allowingreaders to take on more challenging problems as their skill levelsincrease Chapter-by-chapter projects that aid in the visualization ofprobability distributions New coverage of statistical quality control and qualityproduction An appendix dedicated to the use ofMathematica® and a companion website containing thereferenced data sets Featuring a practical and real-world approach, this textbook isideal for a first course in probability for students majoring instatistics, engineering, business, psychology, operations research,and mathematics. Probability: An Introduction with StatisticalApplications, Second Edition is also an excellent reference forresearchers and professionals in any discipline who need to makedecisions based on data as well as readers interested in learninghow to accomplish effective decision making from data.

### Probability , An Introduction with Statistical Applications

Facts101 is your complete guide to Probability , An Introduction with Statistical Applications. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

### Probability

### Numerical Probability

This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance. Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.

### High-Dimensional Probability

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

### The Architecture of Chance

Undergraduate textbooks for statistics courses in the behavioral, biological, and social sciences must devote so much space to the nuts-and-bolts details of statistical methods that they have little left over for the larger conceptual framework of probability theory. This brief, lucid book fills the gap with its intelligible and in-depth explanation of probability, laid out step-by-step in a clear and congenial fashion. Even the student with little background in mathematics will find it readable and accessible.

### Die Wahrscheinlichkeit

### An Introduction to Probability and Statistics

### Understanding Statistics and Probability

A book on statistical theory and applications for undergraduate and graduate students in business, management, economics, social sciences, psychology, medicine, biostatistics and alike, as well as for practitioners. It is a hands-on guide, using computer software and real-world examples as well as Monte-Carlo simulation in order to understand statistical methods and toolboxes. Covers: - Descriptive and Exploratory Statistics and Data Analysis - Probability Theory and Random Variables (Univariate and Multivariate) - Inferential Statistics (Estimation and Hypothesis Testing) - Regression and Applied Statistics (Regression Analysis, ANOVA, Generalized Linear Models) - Copulas - Bayesian Statistics - Statistical Fallacies + Webpage, Lecture Slides and Data on www.statprob.net

### An Introduction to the Theory of Probability

The Theory of Probability is a major tool that can be used to explain and understand the various phenomena in different natural, physical and social sciences. This book provides a systematic exposition of the theory in a setting which contains a balanced mixture of the classical approach and the modern day axiomatic approach. After reviewing the basis of the theory, the book considers univariate distributions, bivariate normal distribution, multinomial distribution and convergence of random variables. Difficult ideas have been explained lucidly and have been augmented with explanatory notes, examples and exercises. The basic requirement for reading this book is simply a knowledge of mathematics at graduate level. This book tries to explain the difficult ideas in the axiomatic approach to the theory of probability in a clear and comprehensible manner. It includes several unusual distributions including the power series distribution that have been covered in great detail. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging. The author is a former Professor of the Indian Statistical Institute, India.

### An Introduction to Probability and Stochastic Processes

Detailed coverage of probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

### An Introduction to Probability and Inductive Logic

An introductory 2001 textbook on probability and induction written by a foremost philosopher of science.

### An Introduction to Probability

### An Introduction to Probability and Mathematical Statistics

An Introduction to Probability and Mathematical Statistics provides information pertinent to the fundamental aspects of probability and mathematical statistics. This book covers a variety of topics, including random variables, probability distributions, discrete distributions, and point estimation. Organized into 13 chapters, this book begins with an overview of the definition of function. This text then examines the notion of conditional or relative probability. Other chapters consider Cochran's theorem, which is of extreme importance in that part of statistical inference known as analysis of variance. This book discusses as well the fundamental principles of testing statistical hypotheses by providing the reader with an idea of the basic problem and its relation to practice. The final chapter deals with the problem of estimation and the Neyman theory of confidence intervals. This book is a valuable resource for undergraduate university students who are majoring in mathematics. Students who are majoring in physics and who are inclined toward abstract mathematics will also find this book useful.

### An Introduction to Probability and Statistical Inference

An Introduction to Probability and Statistical Inference, Second Edition, guides you through probability models and statistical methods and helps you to think critically about various concepts. Written by award-winning author George Roussas, this book introduces readers with no prior knowledge in probability or statistics to a thinking process to help them obtain the best solution to a posed question or situation. It provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. This text contains an enhanced number of exercises and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities. Reorganized material is included in the statistical portion of the book to ensure continuity and enhance understanding. Each section includes relevant proofs where appropriate, followed by exercises with useful clues to their solutions. Furthermore, there are brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises are available to instructors in an Answers Manual. This text will appeal to advanced undergraduate and graduate students, as well as researchers and practitioners in engineering, business, social sciences or agriculture. Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual

### An Introduction to Information Theory

Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.

### Theories of Probability

Theories of Probability: An Examination of Foundations reviews the theoretical foundations of probability, with emphasis on concepts that are important for the modeling of random phenomena and the design of information processing systems. Topics covered range from axiomatic comparative and quantitative probability to the role of relative frequency in the measurement of probability. Computational complexity and random sequences are also discussed. Comprised of nine chapters, this book begins with an introduction to different types of probability theories, followed by a detailed account of axiomatic formalizations of comparative and quantitative probability and the relations between them. Subsequent chapters focus on the Kolmogorov formalization of quantitative probability; the common interpretation of probability as a limit of the relative frequency of the number of occurrences of an event in repeated, unlinked trials of a random experiment; an improved theory for repeated random experiments; and the classical theory of probability. The book also examines the origin of subjective probability as a by-product of the development of individual judgments into decisions. Finally, it suggests that none of the known theories of probability covers the whole domain of engineering and scientific practice. This monograph will appeal to students and practitioners in the fields of mathematics and statistics as well as engineering and the physical and social sciences.

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*An Introduction*

Author: Geoffrey Grimmett,Dominic Welsh

Publisher: OUP Oxford

ISBN: 0191019925

Category: Mathematics

Page: 288

View: 1445

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Publisher: Cambridge University Press

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ISBN: 3663029530

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Category: Mathematical statistics

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ISBN: 0128004371

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ISBN: 0486158446

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