Probability Mathematics

Master Probability with Ease: A Comprehensive Guide for Grades 10, 11, and 12 Learners

This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.

Updated classic statistics text, with new problems and examples
Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material.

In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probabil­ ity, Statistics, and Stochastic Processors, I, II" and published by that Univer­ sity. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a three­ semester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space.

This is the fourth edition of the Mathematics handbook for science and engineering (BETA). Compared to the previous editions a number of additions and corrections have been made. The Mathematics handbook covers basic areas of mathematics, numerical analysis, probability and statistics and various applications. The handbook is intended for students and teachers of mathematics, science and engineering and for profession­ als working in these areas. The aim of the handbook is to provide useful informa­ tion in a lucid and accessible form in a moderately large volume. The handbook concentrates on definitions, results, formulas, graphs, figures and tables and emphasizes concepts and methods with applications in technology and science. The Mathematics handbook is organised in 19 chapters starting with basic concepts in discrete mathematics and ending with chapters on probability and statistics and a miscellaneous chapter. Crossreferences and an extensive index help the user to find required information. We have not included numerical tables of functions which are available on most scientific calculators and pocket computers. We have treated one variable and multi variable calculus in different chapters, because students, usu­ ally, meet these areas in different courses. In formulating theorems and results sometimes all assumptions are not explicitely stated.

This is the fourth edition of the Mathematics handbook for science and engineering (BETA). Compared to the previous editions a number of additions and corrections have been made. The Mathematics handbook covers basic areas of mathematics, numerical analysis, probability and statistics and various applications. The handbook is intended for students and teachers of mathematics, science and engineering and for profession­ als working in these areas. The aim of the handbook is to provide useful informa­ tion in a lucid and accessible form in a moderately large volume. The handbook concentrates on definitions, results, formulas, graphs, figures and tables and emphasizes concepts and methods with applications in technology and science. The Mathematics handbook is organised in 19 chapters starting with basic concepts in discrete mathematics and ending with chapters on probability and statistics and a miscellaneous chapter. Crossreferences and an extensive index help the user to find required information. We have not included numerical tables of functions which are available on most scientific calculators and pocket computers. We have treated one variable and multi variable calculus in different chapters, because students, usu­ ally, meet these areas in different courses. In formulating theorems and results sometimes all assumptions are not explicitely stated.

This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more.