In this post, we will see the book Applied Problems In Probability Theory by E. Wentzel and L. Ovcharov.

# About the book

This book is based on many years of experience of teaching probability theory and its applications at higher educational establishments. It contains many of the problems we ourselves encountered in our

research and consultative work. The problems are related to a variety of fields including electrical engineering, radio engineering, data transmission, computers, information systems, reliability of technical devices, preventive maintenance and repair, accuracy of apparatus, consumer service, transport, and the health service. The text is divided into eleven chapters; each of winch begins with a short theoretical introduction which is followed by relevant formulas.

The problems differ both in the fields of application and in difficulty.

At the beginning of each chapter the reader will find comparatively simple problems whose purpose is to help the reader grasp the fundamental concepts and acquire and consolidate the experience of applying probabilistic methods. Then follow more complicated applied problems, which can be solved only after the requisite theoretical knowledge has been acquired and the necessary techniques mastered.

The book was translated from Russian by Irene Aleksanova and was published in 1986 by Mir Publishers.

Original scan by DLI. Note: Scan quality is inconsistent and is poor (but mostly readable) at places. I will try to get a better scan soon.

You can get the book here.

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# Contents

Authors’ Preface

Preface to the English Edition 7

## Chapter 1

Fundamental Concepts of Probability Theory. Direct Calculation of Probability in an Urn Model 9

## Chapter 2

Algebra of Events, Rules for Adding and Multiplying Probabilities 29

## Chapter 3

The Total Probability Formula and Bayes’s Theorem 65

## Chapter 4

Discrete Random Variables &6

## Chapter 5

Continuous and Mixed Random Variables 112

## Chapter 6

Systems of Random Variables (Random Vectors} 144

## Chapter 7

Numerical Characteristics of Functions of Random Variables 466

## Chapter 8

Distributions of Functions of Random Variables, The Limit Theorems of Probability Theory 217

## Chapter 9

Random Functions 260

## Chapter 10

Flows of Events. Markov Stochastic Processes 324

## Chapter 11

Queueing Theory 863

Appendices 420

Bibliography 432