The book collects a significant portion of the lectures on probability and statistics that have been published on this website.
Visitors to the website have been constantly increasing, and I have received positive feedbacks from many of them, but some readers suggested that the lectures would be easier to study if they were organized and printed as a textbook.
I followed their suggestion and created a textbook that is intended to cover most of the topics that are usually found in intermediate courses in probability theory and mathematical statistics.
The main aim of the book is to be a **time saver**. It collects results and proofs that are hard to find in standard references and are scattered here and there in more specialistic books.

Here are some excerpts from the book reviews on the various Amazon websites (both first and second edition):

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 recomend to people with some knowledge of statistics. The world appreciates your work Marco. I would also recomend it to MSc and PhD students.

Michail, December 8, 2012.

Title: Lectures on probability theory and mathematical statistics.

Edition: Second edition.

Author: Marco Taboga.

Publisher: Amazon CreateSpace.

Number of pages: 656.

Number of chapters: 79.

The book

Most of the learning materials found on this website are now available in a traditional textbook format.

Featured pages

- Beta distribution
- Law of Large Numbers
- Poisson distribution
- Exponential distribution
- F distribution
- Maximum likelihood

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Main sections

- Mathematical tools
- Fundamentals of probability
- Probability distributions
- Asymptotic theory
- Fundamentals of statistics
- Glossary

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