Probability and Random Variables: A Beginner's Guide

ISBN-13: 9780521644457 / Angielski / Miękka / 1999 / 382 str.

David Stirzaker

Opis

This concise introduction to probability theory is written in an informal, tutorial style with concepts and techniques defined and developed as necessary. After an elementary discussion of chance, Stirzaker sets out the central and crucial rules and ideas of probability including independence and conditioning. Counting, combinatorics, and the ideas of probability distributions and densities follow. Later chapters present random variables and examine independence, conditioning, covariance, and functions of random variables, both discrete and continuous. The final chapter considers generating functions and applies this concept to practical problems including branching processes, random walks, and the central limit theorem. Examples, demonstrations, and exercises are used throughout to explore the ways in which probability is motivated by, and applied to, real life problems in science, medicine, gaming and other subjects of interest. Essential proofs of important results are included. Assuming minimal prior technical knowledge on the part of the reader, this book is suitable for students taking introductory courses in probability and will provide a solid foundation for more advanced courses in probability and statistics. It is also a valuable reference to those needing a working knowledge of probability theory and will appeal to anyone interested in this endlessly fascinating and entertaining subject.

Recenzje

'This book is an ideal text for an introductory university course in probability … This is a very-well written book. the content and the informal tutorial style are such that the book can be strongly recommended.' Jordan M. Stoyanov, Zentralblatt MATH

Spis treści

1. Introduction; Part A. Probability: 2. The rules of probability; 3. Counting and gambling; 4. Distributions: trials, samples and approximation; Part B. Random Variables: 5. Random variables and their distributions; 6. Jointly distributed random variables; 7. Generating functions; 8. Appendix: hints and solutions for selected exercises and problems.