Customer Reviews

Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions

5 star:		(3)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

Instructors and students alike will find here a real treasure of exercises in probability and statistics. A broad range of topics is covered. Solutions for typical examples are provided at the start of each section. Apart from the more than 1000 problems (the answers and solutions to all of which are provided at the back), the book contains problems both simple and challenging. I personally found some of the latter most fascinating.

Sveshnikov gives a very brief introduction to each topic, with definitions and formulae presented without proofs, followed by a couple of worked examples, and a couple pages of problems. Answers to all problems are in the back, making it ideal for self-study.
If you have not studied any statistics before, you might want to start with a book that gives more explanation, such as Bulmer, "Principles of Statistics."
This book makes use of calculus in many sections. For interesting probability problems with less advanced math, you might try Mosteller, "Fifty Challenging Problems in Probability."
If you take the time to work through a number of problems from each chapter, you can learn how to apply probability and statistics to a wide variety of problems. The equations I derived for the thesis I'm working on are the topic of chapter 6!

I am enjoying working through this book. Each section contains several worked examples, and problems, which supposedly correlate with the examples. In several situations, though, there is a simpler solution than following the example. Unfortunately, this is only one of several problems. For instance:
* Asks that you prove a statement, which is usually false (A'B u B'A = A' n B'). Only one found so far.
* Some solutions don't exactly correspond with the questions (i.e . the numbers used in the solution are different from the question.) Easily recognized.
* Ambiguous wording of problems (what is the difference between a boat moving "along a bay" vs. "across the same bay"?) This could be due to poor translation. Very frustrating. (And really why I can't give this book five stars)
* Some complex problems have an answer, but no solution, so you aren't sure if the mistake is yours or the book's.
* Different notation. (Uses D and M rather than E and Var) Easily adapted to.

Despite these problems, I am finding working through these problems to be a very rewarding experience. Solving Buffon's needle problem was definitely the highlight of my day.

Actually, I really like this book. I realised that it can be used as a text itself. It can used with advanced probability and math stats courses or in graduated courses. I highly recommend this book.