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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Saeed Ghahramani |

ISBN: | 9780429856280 0429856288 9780429457951 0429457952 |

OCLC Number: | 1049827041 |

Notes: | Includes index. |

Description: | 1 online resource |

Contents: | Axioms of Probability -- Introduction -- Sample Space and Events -- Axioms of Probability -- Basic Theorems -- Continuity of Probability Function -- Probabilities and Random Selection of Points from Intervals -- What Is Simulation? -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Combinatorial Methods -- Introduction -- Counting Principle -- Number of Subsets of a Set -- Tree Diagrams -- Permutations -- Combinations -- Stirlings Formula -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Conditional Probability and Independence -- Conditional Probability -- Reduction of Sample Space -- The Multiplication Rule -- Law of Total Probability -- Bayes Formula -- Independence -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Distribution Functions and Discrete Random Variables -- Random Variables -- Distribution Functions -- Discrete Random Variables -- Expectations of Discrete Random Variables -- Variances and Moments of Discrete Random Variables -- Moments -- Standardized Random Variables -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Special Discrete Distributions -- Bernoulli and Binomial Random Variables -- Expectations and Variances of Binomial Random Variables -- Poisson Random Variable -- Poisson as an Approximation to Binomial -- Poisson Process -- Other Discrete Random Variables -- Geometric Random Variable -- Negative Binomial Random Variable -- Hypergeometric Random Variable -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Continuous Random Variables -- Probability Density Functions -- Density Function of a Function of a Random Variable -- Expectations and Variances -- Expectations of Continuous Random Variables -- Variances of Continuous Random Variables -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Special Continuous Distributions -- Uniform Random Variable -- Normal Random Variable -- Correction for Continuity -- Exponential Random Variables -- Gamma Distribution -- Beta Distribution -- Survival Analysis and Hazard Function -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Bivariate Distributions -- Joint Distribution of Two Random Variables -- Joint Probability Mass Functions -- Joint Probability Density Functions -- Independent Random Variables -- Independence of Discrete Random Variables -- Independence of Continuous Random Variables -- Conditional Distributions -- Conditional Distributions: Discrete Case -- Conditional Distributions: Continuous Case -- Transformations of Two Random Variables -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Multivariate Distributions -- Joint Distribution of n > Random Variables -- Joint Probability Mass Functions -- Joint Probability Density Functions -- Random Sample -- Order Statistics -- Multinomial Distributions -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- More Expectations and Variances -- Expected Values of Sums of Random Variables -- Covariance -- Correlation -- Conditioning on Random Variables -- Bivariate Normal Distribution -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Sums of Independent Random Variables and Limit Theorems -- Moment-Generating Functions -- Sums of Independent Random Variables -- Markov and Chebyshev Inequalities -- Chebyshevs Inequality and Sample Mean -- Laws of Large Numbers -- Central Limit Theorem -- Chapter Summary -- Review Problems -- Self-Test on Chapter -- Stochastic Processes -- Introduction -- More on Poisson Processes -- What Is a Queuing System? -- PASTA: Poisson Arrivals See Time Average -- Markov Chains -- Classifications of States of Markov Chains -- Absorption Probability -- Period -- Steady-State Probabilities -- Continuous-Time Markov Chains -- Steady-State Probabilities -- Birth and Death Processes -- Chapter Summary -- Review Problems -- Self-Test on Chapter. |

Responsibility: | Saeed Ghahramani. |

### Abstract:

"The 4th edition of Ghahramani's book is replete with intriguing historical notes, insightful comments, and well-selected examples/exercises that, together, capture much of the essence of probability. Along with its Companion Website, the book is suitable as a primary resource for a first course in probability. Moreover, it has sufficient material for a sequel course introducing stochastic processes and stochastic simulation."--Nawaf Bou-Rabee, Associate Professor of Mathematics, Rutgers University Camden, USA "This book is an excellent primer on probability, with an incisive exposition to stochastic processes included as well. The flow of the text aids its readability, and the book is indeed a treasure trove of set and solved problems. Every sub-topic within a chapter is supplemented by a comprehensive list of exercises, accompanied frequently by self-quizzes, while each chapter ends with a useful summary and another rich collection of review problems."--Dalia Chakrabarty, Department of Mathematical Sciences, Loughborough University, UK "This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases. The book's ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding. Because the definitions, theorems, and examples are clearly labeled and easy to find, this book is not only a great course accompaniment, but an invaluable reference." --Joshua Stangle, Assistant Professor of Mathematics, University of Wisconsin - Superior, USA This one- or two-term calculus-based basic probability text is written for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It presents probability in a natural way: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. This book is mathematically rigorous and, at the same time, closely matches the historical development of probability. Whenever appropriate, historical remarks are included, and the 2096 examples and exercises have been carefully designed to arouse curiosity and hence encourage students to delve into the theory with enthusiasm. New to the Fourth Edition: 538 new examples and exercises have been added, almost all of which are of applied nature in realistic contexts Self-quizzes at the end of each section and self-tests at the end of each chapter allow students to check their comprehension of the material An all-new Companion Website includes additional examples, complementary topics not covered in the previous editions, and applications for more in-depth studies, as well as a test bank and figure slides. It also includes complete solutions to all self-test and self-quiz problemsSaeed Ghahramani is Professor of Mathematics and Dean of the College of Arts and Sciences at Western New England University. He received his Ph.D. from the University of California at Berkeley in Mathematics and is a recipient of teaching awards from Johns Hopkins University and Towson University. His research focuses on applied probability, stochastic processes, and queuing theory.

## Reviews

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"This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases. The book's ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding. Because the definitions, theorems, and examples are clearly labeled and easy to find, this book is not only a great course accompaniment, but an invaluable reference." ~Joshua Stangle, University of Wisconsin Read more...

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