Fundamentals of Probability - A First Course

Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.

List of contents

Introducing Probability.- The Birthday and Matching Problems.- Conditional Probability and Independence.- Integer-Valued and Discrete Random Variables.- Generating Functions.- Standard Discrete Distributions.- Continuous Random Variables.- Some Special Continuous Distributions.- Normal Distribution.- Normal Approximations and the Central Limit Theorem.- Multivariate Discrete Distributions.- Multidimensional Densities.- Convolutions and Transformations.- Markov Chains and Applications.- Urn Models in Physics and Genetics.

Summary

Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.

Additional text

From the reviews:
“Throughout the book, the author chooses examples and exercises that are classics in the field of probability … . does an admirable job of combining the rigor necessary for a first course in probability theory while continuing to engage the more applied oriented student’s curiosity with interesting examples and exercises. The book deserves serious consideration for anyone teaching the first course in probability theory or one engaged in applied work who desires a more thorough grounding in the mathematical principles of probability theory.” (Mark A. Mccomb, Technometrics, Vol. 54 (1), February, 2012)
“The present book is a text on the fundamentals of probability at an undergraduate and first-year graduate level for students in science, engineering and economics. … The book has an excellent set of examples and exercises and two appendices on supplementary homework, practice problems, symbols and formulas.” (Andreas N. Philippou, Zentralblatt MATH, Vol. 1211, 2011)

Report

From the reviews:
"Throughout the book, the author chooses examples and exercises that are classics in the field of probability ... . does an admirable job of combining the rigor necessary for a first course in probability theory while continuing to engage the more applied oriented student's curiosity with interesting examples and exercises. The book deserves serious consideration for anyone teaching the first course in probability theory or one engaged in applied work who desires a more thorough grounding in the mathematical principles of probability theory." (Mark A. Mccomb, Technometrics, Vol. 54 (1), February, 2012)
"The present book is a text on the fundamentals of probability at an undergraduate and first-year graduate level for students in science, engineering and economics. ... The book has an excellent set of examples and exercises and two appendices on supplementary homework, practice problems, symbols and formulas." (Andreas N. Philippou, Zentralblatt MATH, Vol. 1211, 2011)

Product details

• Authors: Anirban DasGupta
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.06.2012
• EAN: 9781461425816
• ISBN: 978-1-4614-2581-6
• No. of pages: 450
• Weight: 696 g
• Illustrations: XVI, 450 p.
• Series: Springer Texts in Statistics; Springer Texts in Statistics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Stochastik, A, Mathematics and Statistics, Probability Theory and Stochastic Processes, Probabilities, Stochastics, Probability Theory