Mathematical Expectation -- Functions of Random Variables -- Joint and Conditional Distributions.

This book provides an overview of random variables (RVs) and their applications. The authors begin with mathematical expectation, cumulative distribution function, and functions of RVs, and some applications of conditional expectation follow. The book then discusses transformations of RVs and a simple integral method to find the mean deviation of continuous RVs. Joint probability distributions, do-little method of Jacobians, polar-transformations, Rosenblatt transform, copula-based methods, and its applications are covered. An up-to-date reference list and approximately 225 exercise problems appear in the book. The authors have updated and expanded upon their writing on these topics, which they originally covered in a previous book, Statistics for Scientists and Engineers. In addition, this book: Combines theory with numerical examples to provide a thorough explanation of the topic Includes numerous exercises so that readers can practice applying the concepts within the book Presents an up-to-date reference list and around 225 exercise problems.