For one thing, such mainstays as the central limit theorem and the law of large numbers are idiosyncratic probabilistic beasts, and in the present text these huge creatures piggyback: Roussas introduces the weak law of large numbers in an exercise on p. Chapter 1 is foundational: measure theory and random variables, and the culmination a theorem providing for pointwise approximation of random variables by sequences of simple random variables. Chapter 2 amplifies measure theory, playing measures against point functions. Chapter 3 hits the important theme of sequences of random variables. Chapter 4 gives us integration of a random variable relative to a measure.
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About this title An Introduction to Probability and Statistical Inference, Second Edition, guides you through probability models and statistical methods and helps you to think critically about various concepts. Written by award-winning author George Roussas, this book introduces readers with no prior knowledge in probability or statistics to a thinking process to help them obtain the best solution to a posed question or situation.
It provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. This text contains an enhanced number of exercises and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities.
Reorganized material is included in the statistical portion of the book to ensure continuity and enhance understanding. Each section includes relevant proofs where appropriate, followed by exercises with useful clues to their solutions. Furthermore, there are brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises are available to instructors in an Answers Manual.
This text will appeal to advanced undergraduate and graduate students, as well as researchers and practitioners in engineering, business, social sciences or agriculture. Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual "synopsis" may belong to another edition of this title.
From the Back Cover: An Introduction to Probability and Statistical Inference, Second Edition, introduces readers with no prior knowledge in probability or statistics to a thought process that will guide them toward probability models and statistical methods, and help them to think critically about the various concepts involved.
Roussas earned a B. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes.
Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope.
Introduction to Probability
George G Roussas Introduction to Probability, Second Edition, is written for upper-level undergraduate students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences. With his trademark clarity and economy of language, the author explains important concepts of probability, while providing useful exercises and examples of real world applications for students to consider. After introducing fundamental probability concepts, the book proceeds to topics including special distributions, the joint probability density function, covariance and correlation coefficients of two random variables, and more. 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 Year:.
ISBN 13: 9780128001141
Introduction to Probability