Basic Probability Theory

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486466280
Category : Mathematics
Languages : en
Pages : 354

Book Description
This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.

Basic Probability Theory

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486135195
Category : Mathematics
Languages : en
Pages : 354

Basic Probability Theory

Author: Robert B. Ash
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 360

Book Description
Basic concepts; Random variables; Expectation; Conditional probability and expectation; Characteristic functions; Infinite sequences of Random variables; Markov chains; Introduction to statistics.

Basic Probability Theory with Applications

Author: Mario Lefebvre
Publisher: Springer Science & Business Media
ISBN: 0387749950
Category : Mathematics
Languages : en
Pages : 347

Book Description
The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering. Chapters 2 to 4 cover the probability theory they generally need in their training. Although the treatment of the subject is surely su?cient for non-mathematicians, I intentionally avoided getting too much into detail. For instance, topics such as mixed type random variables and the Dirac delta function are only brie?y mentioned. Courses on probability theory are often considered di?cult. However, after having taught this subject for many years, I have come to the conclusion that one of the biggest problems that the students face when they try to learn probability theory, particularly nowadays, is their de?ciencies in basic di?erential and integral calculus. Integration by parts, for example, is often already forgotten by the students when they take a course on probability. For this reason, I have decided to write a chapter reviewing the basic elements of di?erential calculus. Even though this chapter might not be covered in class, the students can refer to it when needed. In this chapter, an e?ort was made to give the readers a good idea of the use in probability theory of the concepts they should already know. Chapter 2 presents the main results of what is known as elementary probability, including Bayes’ rule and elements of combinatorial analysis.

Basic Principles and Applications of Probability Theory

Author: Valeriy Skorokhod
Publisher: Springer Science & Business Media
ISBN: 3540263128
Category : Mathematics
Languages : en
Pages : 276

Book Description
The book is an introduction to modern probability theory written by one of the famous experts in this area. Readers will learn about the basic concepts of probability and its applications, preparing them for more advanced and specialized works.

Elementary Probability Theory with Stochastic Processes

Author: K. L. Chung
Publisher: Springer Science & Business Media
ISBN: 1475739737
Category : Mathematics
Languages : en
Pages : 332

Book Description
This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.

Understanding Statistics and Experimental Design

Author: Michael H. Herzog
Publisher: Springer
ISBN: 3030034992
Category : Science
Languages : en
Pages : 146

Book Description
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.

An Elementary Introduction to the Theory of Probability

Author: Boris Vladimirovich Gnedenko
Publisher: Courier Corporation
ISBN: 0486601552
Category : Mathematics
Languages : en
Pages : 162

Book Description
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

Introduction to Probability

Author: David F. Anderson
Publisher: Cambridge University Press
ISBN: 110824498X
Category : Mathematics
Languages : en
Pages : 447

Book Description
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

A Basic Course in Probability Theory

Author: Rabi Bhattacharya
Publisher: Springer Science & Business Media
ISBN: 0387719385
Category : Mathematics
Languages : en
Pages : 217

Book Description
Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.