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Probability and Random Variables: Theory and Applications

  • Inspires readers to advance beyond the basic level in probability and random variables.

  • Offers a valuable resource for reviewing familiar concepts, in addition to some unique methods and contents.

  • Enhances readers’ understanding with a total of 330 practice problems, with a complete solution manual.

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eBook USD 84.99
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  • ISBN: 978-3-030-97679-8
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  • Own it forever
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Hardcover Book USD 109.99
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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
  2. Preliminaries

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 1-92
  3. Fundamentals of Probability

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 93-160
  4. Random Variables

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 161-254
  5. Random Vectors

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 255-336
  6. Normal Random Vectors

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 337-414
  7. Convergence of Random Variables

    • Iickho Song, So Ryoung Park, Seokho Yoon
    Pages 415-460
  8. Back Matter

    Pages 461-496

About this book

This book discusses diverse concepts and notions – and their applications – concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for.

Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise.

Keywords

  • Convergence
  • Central Limit Theorem
  • Cumulative Distribution Function
  • Gamma Function
  • Gaussian Random Vector
  • Generalized Distribution
  • Impulse Function
  • Joint Moment of Normal Random Vector
  • Normal Random Vector
  • Price’s Theorem
  • Probability Density Function
  • Probability Mass Function
  • Probability Theory
  • Random Variable
  • Random Vector. Set Theory
  • Singular Function
  • Stable Distribution
  • Statistic
  • Step Function

Authors and Affiliations

  • School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea (Republic of)

    Iickho Song

  • School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, Korea (Republic of)

    So Ryoung Park

  • College of Information and Communication Engineering, Sungkyunkwan University, Suwon, Korea (Republic of)

    Seokho Yoon

About the authors

Iickho Song received the BSE and MSE degrees in electronics engineering fromSeoul National University, Seoul, Korea, in 1982 and 1984, respectively, and the

MSE and PhD degrees in electrical engineering from the University of Pennsylvania,

Philadelphia, PA, USA, in 1985 and 1987, respectively.

In March 1988, Dr. Song joined the School of Electrical Engineering, Korea Advanced

Institute of Science and Technology, Daejeon, Korea, where Dr. Song is currently a Professor. Dr. Song is also a

Professor at Liangjiang International College, Chongqing University of Technology, Chongqing, China.

The research interests of Dr. Song include communications theory, signal detection theory,

and statistical signal processing. Dr. Song is a Fellow of the IEEE and IET.

 

So Ryoung Park received the BS degree in electronics engineering from Yonsei University,

Seoul, Korea, in 1997, and the MSE and PhD degrees in electrical engineering from Korea

Advanced Institute of Science and Technology, Daejeon, Korea, in 1999 and 2002, respectively.

In March 2003, Dr. Park joined the School of Information, Communications, and Electronics

Engineering, the Catholic University of Korea, Bucheon, Korea, where Dr. Park is currently a Professor.

The current research interests of Dr. Park include detection and estimation theory, statistical

signal processing, and wireless communications. Dr. Park is a Senior Member of the IEEE.

 

Seokho Yoon received the BSE, MSE, and PhD degrees in electrical engineering from Korea

Advanced Institute of Science and Technology, Daejeon, Korea, in 1997, 1999, and 2002, respectively.

In March 2003, Dr. Yoon joined the College of Information and Communication Engineering,

Sungkyunkwan University, Suwon, Korea, where Dr. Yoon is currently a Professor.

The research interests of Dr. Yoon include detection and estimation theory and mobile

communications. Dr. Yoon is a Senior Member of the IEEE.

Bibliographic Information

  • Book Title: Probability and Random Variables: Theory and Applications

  • Authors: Iickho Song, So Ryoung Park, Seokho Yoon

  • DOI: https://doi.org/10.1007/978-3-030-97679-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-97678-1

  • eBook ISBN: 978-3-030-97679-8

  • Edition Number: 1

  • Number of Pages: XII, 496

  • Number of Illustrations: 10 b/w illustrations, 94 illustrations in colour

  • Topics: Statistical Theory and Methods, Probability Theory

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-97679-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 109.99
Price excludes VAT (USA)