The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results.The step-by-step approach makes the book easy to understand and ideal for self-study.One of the main aims of the book is to be a time saver: it contains several 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 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, Slutsky'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.
Details e-book Lectures on Probability Theory and Mathematical Statistics - 3rd Edition
🗸 Author(s): Marco Taboga
🗸 Title: Lectures on Probability Theory and Mathematical Statistics - 3rd Edition
🗸 Rating : 4.7 from 5 stars (55 reviews)
🗸 ISBN-10: 1981369198
🗸 ISBN-13: 9781981369195
🗸 Languange: English
🗸 Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
🗸 Supported Devices: Android, iOS, PC and Amazon Kindle
✓ Read as many eBooks you want!
✓ Secure Scanned. No Virus Detected
✓ Thousands of eBooks to choose from - Hottest new releases
✓ Click it and Read it! - no waiting to read eBooks, it's instant!
✓ Keep reading your favorite eBooks over and over!
✓ It works anywhere in the world!
✓ No late fees or fixed contracts - cancel anytime!
Readers' opinions about Lectures on Probability Theory and Mathematical Statistics - 3rd Edition by Marco Taboga
Zelene Hampton
This book was a captivating journey of self-discovery and growth. The protagonist's transformation was so beautifully portrayed, making the story truly unforgettable. The evocative descriptions painted a vivid picture, and the plot's twists and turns kept me intrigued until the very end. A fantastic read that left me feeling both satisfied and wanting more.
Eloise Bailey
This book was an absolute page-turner! The author's descriptive writing brought the world and characters to life in a way that felt incredibly immersive. The plot was filled with suspense and surprises, keeping me on the edge of my seat until the very end. A fantastic read that left me eager to explore more of the author's work.
Wynne Binder
I was enchanted by this book's lyrical prose and mesmerizing narrative. The vivid descriptions transported me to a world of magic and wonder. The characters were multidimensional, with flaws and strengths that made them feel like real people. This book was an unforgettable journey, and I am grateful for the experience it provided.