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Review: John E. Freund's Mathematical Statistics with Applications. By Irwin Miller Marylees Miller. Eighth Edition.

This book is the main textbook in Introduction to Probability course at Statistics and Operation Research department at Kuwait University, here is the course description:
https://drive.google.com/file/d/0B0P5...

[ Hierarchy of the book ]

The book has 14 chapters, 3 Appendix about sums and products and Special Probability formulas, and a Statistical table. I did not particularly apprec

Review: John E. Freund's Mathematical Statistics with Applications. By Irwin Miller Marylees Miller. Eighth Edition.

[ Hierarchy of the book ]

The book has 14 chapters, 3 Appendix about sums and products and Special Probability formulas, and a Statistical table. I did not particularly appreciate the table of contents because it only gives the name of the chapters without the sections in the chapter, so the sections mentioned at the beginning of each chapter not in the table of contents. So because of that, there was a problem with moving between the sections.

[ Contents and writing style ]

I did study the first six chapters, which is almost half of the book.
The book is a primary introduction to probability, so it covers:
* Counting methods.
* Basic probability operations.
* Conditional probability and independence and Bayes theorem.
* Discrete and Continuous Random Variables.
* Moments and Moment-Generating Functions.
* Chebyshev's Theorem.
* Special Distributions like Binomial, Geometric, Gamma, and Normal with their means and variances.
* Joint distributions like Bivariate, Marginal, and Conditional with their means and variances.

The style of the writing is suitable for an introductory but not rigorous. Also, the book does not emphasize the conceptual ideas behind the formulas and the theorems. Even when presenting new topics, he gives the definitions with a brief comment without discussing the idea behind this definition and why it is essential or what is the use of it and the implementation of this definition and how we can relate it with the overall picture. It seems he gives the definitions to go straight up to apply a bunch of formulas, which is not a bad thing; however, it should not be the primary goal.

So, even though the book presents helpful examples to explain the ideas, it is more important to give a bit longer time to discuss the conceptual ideas so that the reader can attain probabilistic reasoning. Related to the previous point, I would recommend reading Statistics without Tears: An Introduction for Non-Mathematicians https://www.goodreads.com/book/show/3... to have firm statistical reasoning.

Also, I would also strongly recommend studying Herbert Enderton lectures in Probability, which covers the same topics in this book so you can watch a specific lecture or the whole series.
https://www.youtube.com/playlist?list...

[ Exercises ]

A pleasant thing to mention that the book has a variety of exercises for each section, and after each chapter, there is a lot of applied exercise that helps the reader to be able to apply the learned tools in life problems. Also, there are some new ideas presented in the exercises, so it is worthwhile to have a look at the exercises.

[ General comments ]

There is a good thing in the book, the sections named "The Theory in Practice," which gives some appreciation to the new tools studied in the chapter and applies them in problems and use some programs like Minitab to get solutions.

The book did not give a serious discussion about Baye's theorem as he did not go in the details and the inference value that gives. I know it is an introductory book; however, Baye's theorem deserves proper treatment. Look, for example, PROBABILITY by Jim Pitman https://www.springer.com/gp/book/9780... how did he present Baye's theorem.

Also, about Baye's theorem, I strongly recomend to watch 3Blue1Brown videos:
Bayes theorem: https://www.youtube.com/watch?v=HZGCo...
and
The quick proof of Bayes' theorem: https://www.youtube.com/watch?v=U_85T....

About the distribution, the book did not discuss the origin of it or why they are in this way; instead, he just presented the probability function then extracted the mean and the variance. It would be a good thing if he spent more time explaining these distributions and their uses. So the reader would appreciate what he is studying and have a decent background about the distributions' theoretical base instead of using them as an input-output process with no meanings.

Marginal note: I am a Mathematics student, so I like to study probability with the context of mathematics, not as applied tools.
Which means there must be a rigorous discussion of the foundation and the inference, not necessarily advance but rigorous, the nearest book I found that have this criterion is:
Introduction to Probability by David F. Anderson, Timo Seppäläinen, and Benedek Valkó.
https://www.cambridge.org/core/books/...

Overall the book will serve the purpose of having a first look in probability, but there will be some serious gaps.

...more

It is a really good introductory book for the subject of statistics. I am from a non-statistics background (though I have studied mathematics) and I find this book really helpful to understand the basics of statistics.

Mar 15, 2014 然毕 rated it did not like it

I have this book (eigth edition). I am confused by the table of contents, below each subtitle, they write their name, are you kidding me ?
For example: 1.introduction (Irwin Miller/ Marylees Miller)...14.Regression and Correlation(Irwin Miller/ Marylees Miller).....Appendix(Irwin Miller/ Marylees Miller)，statistical tables（(Irwin Miller/ Marylees Miller)）
Can someone explain to me why they act like idiots?

This review has been hidden because it contains spoilers. To view it, click here. lkzxlkz

Mar 02, 2013 Jette Stuart rated it it was amazing

This was my first formal introduction to statistics. If you have access to the solutions manual, I highly recommend it for undergraduate practice problems.