An innovative textbook on probability and statistics

Many students use as a reference but think that studying on paper is more productive

Female student distracted by her cell phone


Digital textbooks often provide great learning experiences, but they can lead to inferior outcomes when the computer becomes a source of distractions (e-mail, twitter, etc.). The best outcomes are achieved when a digital textbook is coupled with a paper textbook.

Male student carefully annotating a book with a pencil


Many students like to make annotations on their textbooks and underline important parts. This is done very efficiently on paper, much less on a computer. On the first reading the textbook is personalized with annotations, then the revision process becomes more efficient.

Female student sitting outside and studying a book


Several students prefer to limit the number of hours per day spent in front of a computer screen or reading a tablet. Furthermore, a paper textbook never runs out of battery! Some find it more relaxing. Others just like the look and feel of paper textbooks.

Save time and understand more


The focus is on productivity and understanding


providing you with a deeper than average understanding of the main topics in probability and statistics, while also saving you time.


with several features you won't find in the average statistics textbook.

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Hundreds of examples and solved exercises

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Proofs are never left to the reader

Instructor filling huge blackboard with mathematical symbols
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We show you how to do the tedious algebra

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We do not assume you remember everything

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We strive for rigor and ease of understanding


What people say about the book


Excerpts from book reviews posted on Amazon


This is a great book, I used it as my only text book for my MSc probability and stats course and never needed anything else.

Max Latey, February 5, 2021.


This book covers with detail and clarity topics that are usually poorly covered in most statistics books. The worked problems and examples also make it easier to learn by yourself. Very good.

Lucas Garcez, January 20, 2020.


Fantastic book. I was amazed at the clarity of the book despite its rigor. Also, Dr. Taboga uses an extensive and organized system of referencing back to the earlier pages (if it is required to understand the present material), which I have never seen any author doing with the same efficiency. This saves a lot of my time. God bless him.

Shashwat Tanay, December 29, 2017.


A very good presentation, anticipating possible questions and providing precise and concise answers. Excellent coverage of the necessary background.

Amazon Customer, June 21, 2017.


The style of writing is excellent and the organization of the material is logical. Most of the stats books I have read so far are messy, and often require background knowledge that is not commonly found in courses in science and technology, other than maths. Other books are just super easy and do not cover important results. This book has the right balance. I really recommend it.

ZigZag, June 11, 2017.


I was not disappointed; this book is absolutely fantastic. The material is self-contained and builds from one chapter to the next in a way that increases difficulty and scope without leaving the reader lost and having to resort to Google to claw their way through.

Nathan Martinez, April 7, 2016.


The book is clearly written and it covers basic to intermediate material such as moment generating functions, characteristic functions, Gamma and Beta functions. The big plus of this book is that full proofs are given, whereas in many other books on statistics the proofs are sometimes omitted or are not given in full. At the end of each Chapter there are also a few problems with solutions that are helpful in further understanding the material covered.

P. Papanastasiou, May 6, 2015.


Excellent, compact introduction to mathematical probability, distributions, and the algebra of random variables. Marco Taboga employs concise proofs and an enviable clarity to writing that surpasses many scientific authors on the topic.

Timothy B. Shoaf, February 27, 2015.


The textbook lends itself very well to self study of this subject. Examples and solved exercises are very instructive, and applies the theory to practical cases in a very helpful manner.

Per Anton Ronning, July 19, 2013.


I enjoy the style of writing and the simplicity used in treating each topic. The step by step approach is simple to understand.

Ibegbulem Zebulon, July 10, 2013.


Lectures on Probability Theory and Mathematical Statistics is an excellent text, because it is clearly written, easily readable, covers a lot of ground, and explains things intuitively.

Melissa Herston, June 27, 2013.


This book helps me a lot. It is easy to understand and it is very good for self study as well. Thank you for making such a wonderful book. I have no doubt that this book will help anyone who is learning Probability at mid advanced level.

Cheikh, June 1, 2013.


The book is very well written. It is ideal especially for people who have started reading statistics. It is a collection of many things in statistics nicely written and out together. The examples are simple and nice. I finally found a book to recommend to people with some knowledge of statistics. The world appreciates your work Marco. I would also recommend it to MSc and PhD students.

Michail, December 8, 2012.


Keep exploring Statlect

Explore the main sections

Fundamentals of probability

Probability distributions

Asymptotic theory

Fundamentals of statistics

Matrix algebra

Other mathematical tools

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Exponential distribution

Gamma function

Beta function

Poisson distribution

Almost sure convergence

Chebyshev inequality