Introduction to Probability, Statistics, and Random Processes
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This book introduces students to probability, statistics, and stochastic processes. It can be used by both students and practitioners in engineering, various sciences, finance, and other related fields. It provides a clear and intuitive approach to these topics while maintaining mathematical accuracy.
The book covers:
- Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods
- Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities
- Limit theorems and convergence
- Introduction to Bayesian and classical statistics
- Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion
- Simulation using MATLAB, R, and Python (online chapters)
The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications—such as engineering, finance, everyday life, etc.—are included to aid in motivating the subject.
56 reviews for Introduction to Probability, Statistics, and Random Processes
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Soheil –
I very much liked the structure of the book. The text is very easily readable and math expressions are clear and comprehensive. Each section includes many examples with solutions, which makes it easier for students to test themselves. Solutions are complete and easy to follow, and steps are well explained.
The book starts with vary basic concepts of probability theory, and covers some higher level notions on stochastic process, and Markov chain. It also has a section on concentration which is very useful. These together with the book webpage which provides examples both in MATLAB and R, make the book a very good fit for an undergraduate level textbook on probability.
Ms. Hodge –
The book is an easy, instructive read, and very enjoyable.
Fotchy –
Introduction to Probability, Statistics, and Random Processes and the accompanying website elucidate the fundamentals. As an introductory and self-study resource, it succeeds quite well. From the prospective of a current math undergraduate, there is often no problem with locating supplementary information (think Wikipedia, which is actually cited in this book) and difficult problems (e.g., MIT OCW). What is, however, harder for us to find is a source that clearly and succinctly teaches the fundamentals of a discipline. That is where this book and website can be helpful.
The embedded solutions and proofs are an especially handy feature of the website. Setting them up in this manner makes it easier to actively learn the material, i.e., attempt the examples and proofs first rather than gloss over the solutions. The site also includes calculators for relevant computations, a comprehensive appendix on distributions, and a collection of video lectures to accompany the first few chapters. Overall, it is an excellent self-study or supplementary resource to use to first grasp the basics. If you want to then examine novel applications, rigorous theory, or challenging problems/proofs, then there’s plenty of other free resources available 🙂
Aaron –
I give this book five stars for its clarity and thoroughness. I must say my first reaction was to be surprised at how much better this book is at explaining probability and statistics. On the whole, the writing of the book is rather light and entertaining. For instance, the discussion over convergence and multiple random variables brings a rather complex notion down to something we can identify. Studying this book is ideal for both seniors and graduate students. This book will give all of the students appreciation of all fields actively related to probability and statistics.
The solved problems are very useful. Each non-trivial step in an equation is explained, but not in a frustrating way. There are some problems at the end of each chapter that require deep thinking. However, I think a few more involved ones would be useful. Also, chapter 12 and 13 on the textbook website are very valuable to me in learning simulation using R and MATLAB. These two languages are widely used in my research.
Tong –
This book is great! I love it with so many examples and problems along with solutions. These practices really help me understand the knowledge much better!
K. Casey –
I’m basically a tomeophobe (don’t know if that’s an actual word – I’m just not a big fan of tomes), but this is one of the exceptions. The subject matter is nicely developed and sufficiently complete. I have found it to be excellent for self-study, reference and in general, a delight to read.
MR S S DADWAL –
great book fully explained for the layman
Angela Z. –
Great introductory book for college and beyond. Very clear and precise, the explanations for each concept don’t overexplain or complicate things. The practice problems are comprehensive and solidify the new knowledge without being overwhelmingly difficult. Its price makes it so accesible and the free online resources are great. My only issue is that only instructors can get the solutions manual, so anyone self studying will have to find another way to check their work.
EH –
It is a great book! very nicely written and it was a pleasure to read. It is very clear, light and comprehensive.
John Nedson –
Good book
Tam –
Derek –
Pashro-Nik is an amazing professor. I have had the pleasure of actually being in one of his probability courses.
He wrote this book to make the material more accessible and cheaper for students. You can find the book online for free along with videos of how to approach problems. But, I much prefer the hard copy over PDF.
If you need a laugh, watch his videos with closed captioning. YouTube can’t handle foreign accents.
Mathematical Customer –
Um, as well as I expected.
Calchas –
This is an excellent text on the topic of probability theory, for those totally new or for those reminding themselves of the basic concepts. The book works from many examples rather than abstract definitions, and includes fully worked questions and answers expanding on the material to give the reader a sense he has really understood the topic. References to useful formulae outside of probability theory are explained in detail rather than assumed to be within the domain of the reader’s prior knowledge.
I should say the author has made the text available freely online, at […]
However, the book’s binding is simply glue on the soft spine, which means you need to use something very heavy to hold the book open on the required page; the natural elasticity pulls the book closed quite strongly. A proper binding would avoid this problem. Alternatively you could break the spine to keep it open. I deduct one star for the poor physical quality of the book. The high quality text really deserves a grander physical manifestation than this.
Mathematical Customer –
This book, along with its companion website, are together the most effective way to understand this material. Clear explanations of concepts – check. Problems – check. Solutions – check. Breadth – check. Depth – check. Absolutely wondrous. My hats off to Professor Pishro-Nik.
Jamie –
Good text, very clear with plenty of illustrations and diagrams for visual learners like myself.
Knocking it a star because it came with a page not bound, just stuck inside the book. Thought it was a receipt at first…if I didn’t need it so much then and there I would have returned it, but not worth the wait.
chara11 –
I have read many probability introduction books. This one is far the best you can find among many others. Author put a lot of effort to explain all the topics in the content. Typography is fanstastic (LaTeX way), everybody will realy enjoy the reading. Highly recommended.
sunny –
The book is good with clear and concise chapters. But since the there are no solutions available for the end of chapter problems which are necessary for self study, I cannot use this book to its fullest potential.
Shopper –
Very clear.
Kathleen Mattil –
The examples in the book are very helpful and easy to understand, but they provide very little assistance in solving some of the more complicated end of the chapter problems.
Mathematical Customer –
Really great applied probability, really not so great theory of probability. However as advertised. Just don’t expect any theoretical bonus.
Mathematical Customer –
For context; I am an Economics MSc student – I have been using this book to study as a resource for a pre-sessional statistics module. I have found the book very useful, both for it’s clear explanations and the various problem sets contained within. I also like the fact that several different methods for dealing with problems are presented.
carlos alexandre gomes da silva –
Ali Eslami –
I use this book for a grad course on probability I teach. The book is full of examples and solved problems which I like a lot. Students tell me that the material available online on author’s website is really helpful. I am glad that the author published a solution manual too. I wish the manual could be made available to instructors through the publisher.
Adam –
Although my course content and this textbook was not exactly the same, it covered all of what I was demanded of and went even more in depth!! Freaking amazing, saved me for my probability and statistics electrical engineering course!!!
Mathematical Customer –
Honestly, the most complete book to beginning or reviewing undergrad Probability and Random Variables.
yolandaZ –
I purchased this book one month ago but did not leave any comment the first time I opened this book. I want to actually use this book and do self-learning for a while and then come back here to have a fair comment. The truth is that this book is very practical and useful for both first-time learners and self-learning aces. I like the practice problems at the end of each section. They are worth to be practiced the second or the third times in order to understand the key materials better. I love this book, and I will keep doing the self-learning using this fantastic book written by professor Hossein Pishro-Nik!
Francisco Delgado –
The worked examples throughout the book and the online version of the book are a great value for the price.
Hayford Adjavor –
This textbook is what I’d like to call probability and statistics made easy! I have tried other textbooks on this subject matter, but in my honest opinion, none come close to this text in terms of explanations and pedagogy! Thanks to this textbook and its online resources, I am more confident about this all-important subject which is ubiquitous in our everyday! I will recommend this text to anyone anytime who like to sharpen and/or learn a lot of about this subject at their own time and pace.
Mathematical Customer –
I originally wrote a very lengthy review but to stave boredom on a long trip I re-read this book in its entirety and felt this review needed an edit. Disclaimer: I already had a graduate background in probability before I first encountered this book.This is the best introductory non-measure-theoretic probability book available in the English language. I have read a lot of introductory probability books such Ross, Feller (the introductory chapters in vol 1), Papoulis, Bertsekas, Blitzstein, Tijms, and more. This book stands out as the only one I can recommend in good conscience to someone with a background in nothing more than multivariate calculus and basic linear algebra.It doesn’t matter who you are; whether you are embarking on a probability course at university for the first time, getting into machine learning, grad student looking for a refresher after several years, teaching probability to newcomers, trying to understand options theory, whatever. Want to learn probability? This book is the place to start.My two, and only two, points of criticism are that introduction to probability by Ross explains combinatorics much better, largely because it contains an incredibly long list of combinatorics exercises. Second, that many important concepts are hidden in the exercises. Not necessarily a bad thing because I’d hope newcomers actually do the exercises, but I’d rather they were explained in the main text.In summary, this is THE book to learn probability from. It will create an excellent foundation for you to embark upon any manner of probability topics. I would give it 6 stars if I could. For anyone wondering what to read after this, If you want to go in a very applied route i recommend stochastic processes by Dubrow accompanied by probability for statistics and machine learning by DasGupta as a supplementary reference.
KEN –
it is a little primitive but easy to follow from a generous author who put the whole book in his website. Thanks Hossein,
Erik –
This book saved a lot of head aches when I was taking Probability in University. Unfortunately enough I was assigned another textbook that didn’t help at the slightest. Instead of focusing on theory the author immediately cuts straight to application. I suggest this textbook for anyone who is taking their first probability course.
Sensor2 –
A very good introduction for a cheap price.
Don Estreich –
This is a great introduction to probability, statistics and random variables. I surveyed many books because I will be teaching a course at Sonoma State University on the subject. Pishro-Nik has written a textbook that is easy to understand and has many examples. The fact that it is inexpensive is desirable for students and it is a tested book on the subject.
C You –
This is one of the best textbooks I have ever read.
The chapters are very clearly laid out. Important ideas are explained in terms as simple and clear as possible, and ample examples and exercises with answers were given to help enhancing your understanding.
I took a class of statistics when I was in college many years ago, and in my memory it was a very dry and hard class. This book is really a surprise. I found it quite enjoyable to read this book.
britt –
This is a THICK BOOK!
Bull’s Eye –
This is a brilliant book whose author has gone out of his way to demystify an hitherto convoluted and obscure subject.
Prof Hossein Pishro-Nik is a great teacher both on camera and print. He effortlessly and successfully communicates the fundamentals with such expertise from a student standpoint. His pleasant pedagogy disabuses the dog-eared theorem-lemma of yore. A proper mastery of the first 7 chapters is adequate to provide a solid foundation to explore other advanced realms of probability as applied in different genres of statistics.
Buying this book and investing time reading it, doing the exercises and watching the videos on the book’s webpage amounts to more than a free intellectual gift to any consumer.
ClausVonDerKueste –
I bought the book in 2016. At that time there were no enthusiastic reviews. But already at that time I thought that the book was outstanding in detail and clearness presenting probabilistic concepts. I needed a book accompanying a course in probabilistic programming (WebCHURCH, WebPPL). My math-phobic students come from CS and Psychology. As the book is free online there is no excuse for them to avoid reading.
As my course is Bayesian I recommend chapters 1-7 and 9. Then I move on with excerpts of Held & Bové’s “Applied Statistical Inference: Likelihood and Bayes”, Gelman’s “Bayesian Data Analysis”, or Koller’s “Probabilistic Graphical Models”.
Gabriel T Smith –
I am a first year graduate student in systems engineering taking probability and stochastic processes without a comprehensive background in probability, statistics, or stochastic processes. I’ve been looking for the ‘perfect’ textbook to fill in the gaps as the professor expects us to have had prior knowledge of the material. This textbook is remarkable. Not only is it clear and assumes that the reader has no background in probability, set theory, combinatorics, statistics, but also it is so well-written with excellent examples that illustrate the theorems, definitions, concepts. The textbook covers basic probability, combinatorics, random variables, convergences of random sequences, random processes, discrete and continuous functions (e.g., Poisson) as well as Markov chains, stationarity and other topics with fluidity! Though I might still do poorly in my course (for I found this textbook late in the semester), now that I have it, at least I can learn the material comprehensively on my own!!! What a treasure! My gratitude to the professor who wrote this textbook with such care for the student. And, I wager, that for an advance student in probability, this textbook is an excellent ‘refresher’!
Mathematical Kunde –
Great book, used it for my Introduction to Probability and statistic course, easy to read with lots of examples explaining the theory.
Stone Citadel –
I’ve finished reading this book , which took me 4 months. Although there are some typos, the overall reading experience was good. This book broadens your scope and opens a door for more in-depth math subjects.
RaynLyd –
I got this book for probability and stats for my graduate econometrics class. I liked this book because the author provides lots of problems and solutions. I came from engineering background and did not have math or statistics undergrad, and felt the materials covered in this book was deep enough for my class
Adrián –
Lo que necesitaba para estudiar
Andrew –
Great book. Would recommend as a book for self directed studies, or as a supplement to an existing probability and statistics course. Great price too.
jbrown822 –
A well written and comprehensive intermediate level text.
Rodrigo Viana –
Livro completo para cursos de Probabilidade I e II. Com bastante exercício resolvido e exemplos. Muito completo na área de demonstrações também. Vale a pena.
Mathematical Customer –
If you give it enough time this book has a lot to offer.
Hassam Hayek –
Great book
Mathematical Customer –
A very useful book for a beginner. It can also be used for people who want to refresh their knowledge on the subject. An online version of the book is available on the author’s website. Going through book is useful.
Jordan E. –
This is the textbook of the education utopia that would exist if all authors were as enthusiastic, dedicated, and competent as Hossein Pishro-Nik. Why? In these pages, you will find no over-reliance on mathematics, plenty of worked examples, and absolutely no expense spared in the preparation of this masterpiece. You will instead find a beautiful journey to actually understanding probability and statistics.
1. How does the author explain things without sacrificing rigor? First, by using intuitive arguments. Then, when appropriate, using pictures that make the arguments even more intuitive and obvious. Finally, he comes in for the kill with the mathematics, making the connection to the previous intuitive examples and pictures clear.
2. How does the author make sure you actually learn the material? Worked example after worked example. I have done every single one so far (I count at least 50) and I’m not even done with chapter 1. Each subsection is rich with worked examples immediately when they become useful (if the explanations weren’t so elegant and beautiful it would be reminiscent of a Schaum’s outline), in addition to extra worked problems at the end of each sub-chapter, in ADDITION TO problems without answers at the end of each chapter.
As if this weren’t enough, there are accompanying YouTube lectures, and the entire material of the textbook is available for free on the internet. It’s so perfect it actually made me cry.
Kevin –
This book is a lot better organized in its presentation of information than many probability books like it. It isn’t $200+ either so I applaud the author on all fronts: providing down to earth explanations, many worked out problems, at an accessible price.
Yalin –
a great book
I love it
The printing quality is not so good
Mathematical Customer –
This probability book focuses on the intuition, rather than rigorous proof and logic of probability. If you are stats graduate student, this may not be the choice. But if you think one year of college calculus can allow you to understand the more advanced concept of probability, you certainly underestimate how deep the water of maths and stats is, I would recommend you to spend some time to read this book first
qirong29 –
It’s impossible to give a fair review of a voluminous book on any maths text book because it takes time to go through it and I have not been able to do that in such a short time expected of me!
Traves W. Wood –
This textbook on probability is very simple and gradual. It starts with describing sets and slowly moves into probability. It assumes you know nothing about it from the beginning but appears to be thorough. The only problem is the binding which falls apart not much longer than when you crack open the book open. I got mine rebound through another vendor and it cost as much as the book itself but well worth it. I will probably reference this book for years.
A.M –
A very good book for self learning, written in a lucid manner. Very useful but sometimes oversimplified. Overall a pretty good book for statistical science.