Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider. This edition demonstrates the applicability of probability to many human activities with examples and illustrations. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; special distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Law of Large Numbers; the Central Limit Theorem; and statistical inference. Each section provides relevant proofs, followed by exercises and useful hints. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site. This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences. Demonstrates the applicability of probability to many human activities with examples and illustrations Discusses probability theory in a mathematically rigorous, yet accessible way Each section provides relevant proofs, and is followed by exercises and useful hints Answers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site
The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level.
Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more.
Introduction to Probability
Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided.
The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC).
The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and ...
Market_Desc: This book is intended for Upper Seniors and Beginning Graduate Students in Mathematics, as well as Students in Physics and Engineering with strong mathematical backgrounds.
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability.
The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, ...