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Lectures on Probability Theory and Mathematical Statistics - 2nd Edition, by Marco Taboga
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This book is a collection of lectures on probability theory and mathematical statistics. It provides an accessible introduction to topics that are not usually found in elementary textbooks. It collects results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books.
The main topics covered by the book are as follows.
PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions.
PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions.
PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions.
PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart.
PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions.
PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutski's Theorem.
PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.
- Sales Rank: #443721 in Books
- Published on: 2012-12-08
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x 1.48" w x 7.00" l,
- Binding: Paperback
- 656 pages
Most helpful customer reviews
9 of 9 people found the following review helpful.
clearly written, easily readable, covers a lot of ground, and explains things intuitively
By Melissa Herston
In compliance with FTC guidelines; I received the book for free through Goodreads First Reads.
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.
After going through this book and looking at some other comparable titles, I have to come to the conclusion that this is an excellent text on the topic of Probability Theory and Mathematical Statistics. At 600 plus pages the book is quite long, but the sheer amount of material covered is simply astounding.
This book is well-organized and a good reference text. The book does not assume that the reader is familiar with the topic, but rather starts with the simplest solutions and builds from there. I felt the book is self-contained enough for readers who have not heard of the topic before to get a good idea of it.
There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. The author goes to great lengths to make every concept clear to the reader.
This is a book for those who are interested in probability theory and want to gain a broader understanding of the subject matter. This book is well-organized and is one of the clearest and most readable books on the topic. This book is very full and is a very good resource on the topic.
5 of 5 people found the following review helpful.
Very good book!
By Cheikh
I don't like to review my books, but 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.
2 of 2 people found the following review helpful.
Necessary and Sufficient.
By Timothy B Shoaf
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.
If you need to learn probability for simulation, data science, etc., then start here.
After this I would head to the Springer series on statistics.
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