Introduction to Probability
Charles Grinstead, Swarthmore College
J. Laurie Snell, Dartmouth College
Pub Date: 1997
Publisher: American Mathematical Society
Conditions of Use
There is a table of contents that breaks up the chapters into subtopics, also. There is an index. Not much depth in some areas. There isn't much read more
There is a table of contents that breaks up the chapters into subtopics, also. There is an index. Not much depth in some areas. There isn't much talked about with certain graphics, aka defining histograms and pie charts. Hypothesis testing is limited. There are no solutions in the back of the book to the chapter problems. Correlation? Probability is covered well. Statistics (aka Prob and Stats)?
The book does seem to be free of errors.
The book's relevance and longevity shouldn't be a problem. All information is relevant to the topic. I read the online version. So, one would think that any updates would be rather easily accomplished.
The book wasn't very clear for me. I noticed several times where, for example, individual cases were listed simply within the formatting of the paragraph, where these should probably be outlined, with bullet-points. Or, definitions are given within the framework of the paragraphs, where these should probably be separated from the paragraph, given their own spaces in the text. Even though important terms may be italicized, it can still be difficult to identify them within the readings. Some of the symbols, you have to take your time to make sure you understand just what it is describing.
The textbook does seem to be consistent in its use of terminology and framework. It does show consistent structure, rather than going "hodge podge" every once in a while.
Each chapter in the book does show suptopics on the table of contents. As for re-ordering the chapters, that may have something to do with how the individual instructor conducts the class. As in, if the instructor re-orders the material, they are probably going to have to provide some of their own introduction material for each chapter.
The flow tends to be a bit tedious at times. Some steps and/or terms are written in the format of the paragraphs, themselves, and not set apart from the rest of the writing.
The interface is decent. Some of the charts and tables are 2-4 pages off. But, the way the author did many of the graphics, he grouped many of the graphics together on certain pages. Computer programs are mentioned throughout the examples, but there are no computer codes or programs listed anywhere.
The book's grammar was fine. Very well written in this aspect.
There are seemingly no distinguishing cultural insensitivities.
I felt this textbook could do more. For the price, free, you can't beat it. However, considering as a student, to prepare me for future coursework and work on the job, I believe this textbook leaves much out. I remember taking a course with a book like this; I had to end up taking a separate Statistics class, also, because the course was certain statistics work. A lot of the symbolism comes up on you right away; you really have to take the time to understand the meaning of it. The missing information could be covered by a good instructor, but then there wouldn't be a need for a textbook in those parts. With as many times computer programs were referenced, it would have been nice to actually see the code for these programs at times, at least.
The book covers all areas in a typical introductory probability course. The course would be appropriate for seniors in mathematics or statistics or read more
The book covers all areas in a typical introductory probability course. The course would be appropriate for seniors in mathematics or statistics or data science or computer science. It is also appropriate for first year graduate students in any of these fields.
The book is very accurate.
Content is up-to-date. In fact, the way simulations are used to illustrate important concepts in probability and statistics is now more relevant that ever ! the emerging focus on computing and computing-related areas like the field of Data Science and Data Analytics or Big Data makes this book and important textbook or resource. So, this is the right book or resource and No Need to Re-invent the Wheel!!!!
The book is very clear and smooth. Everything is classic or traditional except few places where I noticed a difference of what I am used to see: the authors used a unique notation, m(x), for the distribution function (cdf) in the discrete case compared to that for the continuous case. Also,I am not sure that the selected vector and complement notations are commonly used.
The book is consistent and the material flows nicely! the important concepts are introduced and revisited many times and sometimes different ways! I love the connection made with other areas! I love the use of Paradoxes.
Modularity is another major strength of the book! Although the material is nicely connected but but once can easily select to cover certain parts and skip others without creating gaps or difficulties in the students leering. The flow of the coverage and the nature of the probability area help in this matter. You can easily treat or cover the discrete random variables separately and select the related material without any difficulties. You can do the same thing for the continuous case. You can leave some of the challenging examples that include some of the paradoxes that maybe challenging for students! You can also easily and smoothly teach or assign the history and development of the selected topics as reading s without making it as a part of the graded course!
Overall, the material is presented in a smooth way! but that is not necessarily the order I would go with when i cover these topics. Of course that is a matter of style, depending on the audience, I think it is easier to teach the material in Ch10 (moment generating functions), then may be add a section about movements. I would probably slightly modify it. I would point at few other things later!
The book is free of any interface issues.
No grammatical errors
The book is written with examples and problems that are very relevant to the culture we are in. Examples form the business world (examples include insurance coverage and insurance-related problems, gambling and lottery, sports, etc.)
Yes, I have specific comments that maybe useful to the authors: First: Thank you: Thank you for writing such a wonderful book. It is very clear, that the standards you held are really high and the timing of the book is unbelievable appropriate! with the new emerging statistical fields, this book should be used in the core courses! Second: I have few specific suggestions/few typos that maybe useful. If you are interested, please let me know.
The book covers the fundamentals of probability theory with quite a few practical engineering applications, which seems appropriate for engineering read more
The book covers the fundamentals of probability theory with quite a few practical engineering applications, which seems appropriate for engineering students to connect the theory to the practice. Each chapter contains realistic examples that apply probability theory to basic statistical inference and naturally connect to the Monte Carlo simulations and graphical illustration of the probability distributions and probability density functions. Students with basic calculus and discrete math can easily follow the development of probabilistic modeling and important properties of the popularly used probability distributions. Only the ergodic Markov chain and random walk appear challenging for the undergraduate students to comprehend without the formal introduction of stochastic process.
I do no see any apparent error in the examples covered by this book.
The book can serve as an introduction of the probability theory to engineering students and it supplements the continuous and discrete signals and systems course to provide a practical perspective of signal and noise, which is important for upper level courses such as the classic control theory and communication system design. The material seems up-to-date and may be appealing to students with experience of Matlab to simulate various random events including the Markov chain and random walk covered in the later chapters.
The book is well written with many interesting exercise problems for students to enhance their understanding. It would be nice to provide a few solutions to the selected problems.
The terminology and framework used in the book are consistent.
The book can be divided and/or regrouped easily to fit the need for self-study. The discrete and continuous random variables and popularly used distributions can be summarized in separate tables (e.g., putting in the appendix).
The book is well organized with coherent logical development. It would be nice to add a brief introduction to continuous time and discrete time stochastic processes before introducing the Markov chain and random walk.
The book has many index terms but not available for click-through in the electronic format.
I do not see any grammatical problem.
I do not see any cultural issue in the examples used to demonstrate the probability theory.
This is a very nice introduction book to probability theory without using axiomatic and/or set theoretic coverage of the probability. It contains many interesting examples to demonstrate how to apply a probabilistic modeling or statistical procedure to study the real world phenomena. The integration with some software (such as Matlab) would provide better visualization of the random events, distribution and statistical properties of the random variable/process.
The book consists of 12 chapters, 3 appendices with tables and index. It is designed for an introductory probability course, for use in a standard read more
The book consists of 12 chapters, 3 appendices with tables and index. It is designed for an introductory probability course, for use in a standard one-term course, in which both discrete and continuous probability is covered. This book covers a little bit more than I would normally cover in a probability class (Markov chains and random walks) and omits nothing that I would normally cover. All subject areas address in the Table of Contents are covered thoroughly.
The book is mathematically accurate as far as I can tell. Examples are worked out in full detail throughout the text. In the earlier version were some mistakes, but have been corrected (errata is available on the website). All of these errors have been corrected in the current web version.
The content is as up-to-date as any introductory probability textbook can reasonably be. In terms of longevity, the fact that the text of the book is stored in LaTeX ensures that the text will be useful for a long time to come. Updates will be straightforward to implement. There are over 600 exercises in the text. There are exercises to be done with and without the use of a computer and more theoretical exercises. A solution manual is available to instructors from website (odd-numbered exercices) or from the authors. In the text the computer is utilized in several ways: simulation, graphical illustration and to solve problems that do not lend to closed-form formulas. All programs used in the text have been written in TrueBASIC, Maple, and Mathematica.
I think that the text in this book is extremely clear, which is great for a first course in probability. It helps a large number of figures illustrating the discussed ideas. Authors have tried to present probability without too much formal mathematics but without sacrificing rigor. They have tried to develop the key ideas to provide a variety of interesting applications in normal live.
The text is consistent in its terminology, both internally and globally.
The text is divided into small subsections with separate exercices for students to read (there are easily be used as modules).
The organization is fine. The book presents all the topics in an appropriate sequence. I expect that instructors using this book would be using the material in the presented order (maybe Combinatorics first).
The interface is OK. I didn't experience any problems. The lack of color graphics even in digital version (few times authors use light blue color). I reviewed using the pdf version of the book. This does not have a linked table of contents, which would allow direct access to the sections. I wish the pdf file had this functionality. The lack of hyperlinks is somewhat troublesome.
I found no grammatical errors in this textbook (but English is not my native language). It is very well written.
No portion of this text appeared to me to be culturally insensitive or offensive in any way, shape, or form.
I think that this textbook provides a great introduction to probability! With such textbook available to students for free, I do not see any reasons to force my students to purchase a different textbook. My only complaint concerns the software. I would have preferred programs to be written in the language R. There are numerous very interesting historical comments in the text.
Table of Contents
- Chapter 1: Discrete Probability Distributions
- Chapter 2: Continuous Probability Densities
- Chapter 3: Combinatorics
- Chapter 4: Conditional Probability
- Chapter 5: Distributions and Densities
- Chapter 6: Expected Value and Variance
- Chapter 7: Sums of Random Variables
- Chapter 8: Law of Large Numbers
- Chapter 9: Central Limit Theorem
- Chapter 10: Generating Functions
- Chapter 11: Markov Chains
- Chapter 12: Random Walks
About the Book
Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.
This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a form understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.
For use in a standard one-term course, in which both discrete and continuous probability is covered, students should have taken as a prerequisite two terms of calculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theory is necessary.
The text can also be used in a discrete probability course. The material has been organized in such a way that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization dispels an overly rigorous or formal view of probability and o?ers some strong pedagogical value in that the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. For use in a discrete probability course, students should have taken one term of calculus as a prerequisite.
Very little computing background is assumed or necessary in order to obtain full benefits from the use of the computing material and examples in the text. All of the programs that are used in the text have been written in each of the languages TrueBASIC, Maple, and Mathematica.
About the Contributors
Charles M. Grinstead, Professor, Department of Mathematics and Statistics, Swarthmore College.
James Laurie Snell, often cited as J. Laurie Snell, was an American mathematician. A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995.