This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus. Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.
The main intended audience for this book is undergraduate students in pure and applied sciences, especially those in engineering.
For a standard two sample t-test, the signal to noise ratio is called Cohen's d, which is estimated from data as (see Chap. 3): d = . Cohen's d tells you how easily you can discriminate different means. The mean difference is in the ...
In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution.
Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes.
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability.
This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering.
The book is an introduction to modern probability theory written by one of the famous experts in this area.
This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.
This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field.
Clear, readable style Solutions to many problems presented in text Solutions manual for instructors Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics No knowledge of general ...