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Introduction to Probability: Models and Applications, N. Balakrishnan, Markos V. Koutras and Konstadinos G. Politis, John Wiley & Sons, 2020, xiii 608 pages, $140.00, hardcover ISBN: 978‐1‐1181‐2334‐8
International Statistical Review ( IF 2 ) Pub Date : 2020-04-12 , DOI: 10.1111/insr.12368
Jorma K. Merikoski 1
Affiliation  

Readership: Teachers and students of a first course in probability.

Chapters: 1. The Concept of Probability, 2. Finite Sample Spaces – Combinatorial Methods, 3. Conditional Probability – Independent Events, 4. Discrete Random Variables and Distributions, 5. Some Important Discrete Distributions, 6. Continuous Random Variables, 7. Some Important Continuous Distributions. Appendices: A. Sums and Products, B. Distribution Function of the Standard Normal Distribution, C. Simulation, D. Discrete and Continuous Distributions.

Each chapter

… contains a section ‘Computational Exercises’ (some are examples).

… ends in a section ‘Applications’ (actually ‘Application’). They are 1. System Reliability, 2. Estimation of Population Size: Capture‐Recapture Method, 3. Diagnostic and Screening Tests, 4. Decision Making Under Uncertainty, 5. Overbooking, 6. Profit Maximization, 7. Transforming Data: The Lognormal Distribution.

… begins by introducing some pioneer of probability who contributed to the topic discussed in the chapter. They are 1. Kolmogorov, 2. Pascal, 3. Bayes, 4. Markov, 5. Bernoulli, 6. Laplace, 7. Gauss.

… includes an abundance of exercises. Each section ends to exercises, mostly classified into two groups: A (routine) and B (more advanced).

… contains a section titled ‘Self‐assessment Exercises’ (true‐false and multiple choice questions) and a section containing ‘Review Problems’.

The first author has much experience in writing textbooks. The second author has written in Greek a book on probability, which is the predecessor of the current book. So the goal the authors put forth in the preface certainly seems reachable: ‘It is our sincere hope that instructors find this textbook to be easy‐to‐use for teaching an introductory course on probability, while the students find the book to be user‐friendly with easy and logical explanations, plethora of examples, and numerous exercises (including computational ones) that they could practice with!’

A plethoraof examples and exercises indeed exists (including many good ones). In my opinion, this is the main merit of the book. But the exercises have no solutions, even no answers or hints. The purpose of adopting this strategy is unclear. If the authors think that there is no space left for them, they could have cut down on the material in favour of some worked out solutions and hints to selected problems. If the authors plan to publish a solution manual separately, this plan should have been mentioned in the preface.

This book is indeed user‐friendly.It gives easy and logical explanationsto basic topics. For students of an introductory course, this may suffice so the book definitely helps them to have success. Of course, the reader encounters proofs and definitions that are more complex and advanced in nature. It seems to me that the authors have managed quite well with most of them, too.

A few exceptions appear, however, of which I give two examples. I enjoyed reading about the definition of probability (relative frequency, axiomatic and classical) in Chapters 1 and 2 but did not feel the same in reading about the definition of a continuous random variable in Section 6.1. Although absolute continuity is beyond the scope of the present book, I think that ‘this is absolute continuity—let's forget it' is not enough. A (very intuitive) brief discussion on absolute continuity (and also on the Lebesgue integral) would have increased the value of the book.

I also enjoyed reading about the normal distribution in Section 7.2 but excluding the (very intuitive) proof of

e x 2 / 2 d x = 2 π
on pp. 503–504. The authors speak about the proof of dx dy = r dθ dr, which, however, is not an exact mathematical formula and therefore has no proof. Two figures, where a circle is divided into dx dy's by horizontal and vertical lines in the first, and into r dθ dr by concentric circles and their radii in the second, would have enabled easy visualization of the change of variables.

This reviewer finds the book easy‐to‐use and looks forward to the appearance of its second volume (informed in the preface) for the second course in probability.



中文翻译:

概率概论:模型与应用》,N.Balakrishnan,Markos V.Koutras和Konstadinos G.

读者群尝试第一门课程的老师和学生。

章节:1.概率概念; 2.有限样本空间–组合方法; 3.条件概率–独立事件; 4.离散随机变量和分布; 5.一些重要的离散分布; 6.连续随机变量; 7.一些重要的连续分布。附录:A.求和和乘积,B.标准正态分布的分布函数,C.模拟,D.离散分布和连续分布。

每章

…包含“计算练习”部分(其中一些是示例)。

…在“应用程序”部分(实际上是“应用程序”)结尾。它们是1.系统可靠性,2.人口规模估计:捕获-重新捕获方法,3.诊断和筛选测试,4.不确定性下的决策,5.超额预订,6.利润最大化,7.转换数据:对数正态分布。

…首先介绍一些概率先驱,他们为本章中讨论的主题做出了贡献。他们是1.科尔莫哥洛夫,2.帕斯卡,3.贝叶斯,4.马尔可夫,5.伯努利,6.拉普拉斯,7.高斯。

…包括大量练习。每个部分以练习结束,主要分为两类:A(常规)和B(高级)。

…包含标题为“自我评估练习”(对错和多项选择题)的部分和包含“复习问题”的部分。

第一作者在编写教科书方面有丰富的经验。第二作者用希腊语写了一本关于概率的书,这是本书的前身。因此,作者在序言中提出的目标肯定可以实现:“我们衷心希望老师们认为这本教科书易于使用,可以教授有关概率的入门课程,而学生们则认为这本书是用户-友好且简单易懂的解释,大量示例以及可以练习的众多练习(包括计算练习)!”

一个大量的例题和习题确实存在(包括许多好的)。我认为,这是本书的主要优点。但是练习没有解决方案,甚至没有答案或提示。采用这种策略的目的尚不清楚。如果作者认为没有剩余空间,他们可能会减少材料,而采用一些可行的解决方案和某些问题的提示。如果作者计划单独发布解决方案手册,则应该在序言中提到该计划。

这本书确实是用户友好的。它为基本主题提供了简单而合理的解释。对于入门课程的学生来说,这可能就足够了,因此这本书绝对可以帮助他们取得成功。当然,读者会遇到本质上更为复杂和高级的证明和定义。在我看来,作者中的大多数人也做得很好。

但是,有一些例外情况,我举两个例子。在第1章和第2章中,我很喜欢阅读有关概率(相对频率,公理和经典)的定义的知识,但在阅读第6.1节中关于连续随机变量的定义时,我的看法并不相同。尽管绝对连续性超出了本书的范围,但我认为“这是绝对连续性-忘记它”是不够的。关于绝对连续性(以及关于勒贝格积分)的(非常直观的)简短讨论会增加这本书的价值。

我也很喜欢阅读第7.2节中关于正态分布的内容,但不包括(非常直观)的

- Ë - X 2 / 2 d X = 2 π
在第503-504页。作者谈论了dx dy = rdθdr的证明,但是,这不是精确的数学公式,因此没有证明。两个数字(第一个数字通过水平线和垂直线将圆划分为dx dy,第二个数字将其通过同心圆及其半径划分为rdθdr)将使可视化变量变化变得容易。

这位审稿人认为这本书易于使用,并期待第二本书概率第二本书的出现(见前言)。

更新日期:2020-04-12
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