Fundamentals of Probability With Stochastic Processes, 4/e (Hardcover)

Saeed Ghahramani

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商品描述

本書序言

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 problems

本書特色

"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.

商品描述(中文翻譯)

本書序言

第四版新增內容:
●新增538個例子和練習,幾乎全部都是在現實情境中應用的
●每個章節結束時的自我測驗和每個章節結束時的自我測試,讓學生檢查他們對材料的理解程度
●全新的附屬網站包含額外的例子,以及前幾版未涵蓋的相關主題和更深入研究的應用,還有測驗題庫和圖片幻燈片。它還包含了所有自我測試和自我測驗問題的完整解答

本書特色

「Ghahramani的第四版書籍充滿了有趣的歷史注解、深入的評論和精心選擇的例子/練習,共同捕捉了概率的本質。配合附屬網站,這本書非常適合作為概率第一課的主要資源。此外,它還有足夠的材料供後續課程使用,介紹隨機過程和隨機模擬。」
- Nawaf Bou-Rabee,美國羅格斯大學卡姆登分校數學副教授

「這本書是一本關於概率的優秀入門書,同時也包含了對隨機過程的深入解說。書中的內容流暢易讀,是一個解決問題的寶庫。每個章節中的每個子主題都有一個全面的練習題清單,並且經常附有自我測驗,而每個章節結束時都有一個有用的摘要和豐富的複習問題集。」
- Dalia Chakrabarty,英國拉夫堡大學數學科學系

「這本教科書全面而嚴謹地介紹了基礎概率,包括離散和連續的情況。書中豐富的練習題目為教師和學生提供了大量的練習和工具,以提高他們的理解能力。由於定義、定理和例子清晰標註且易於查找,這本書不僅是一個很好的課程輔助資料,也是一本寶貴的參考書。」
- Joshua Stangle,美國威斯康辛大學超級數學助理教授

這本以一學期或兩學期為基礎的微積分概率基礎教材適用於數學、物理科學、工程、統計學、精算學、商業和金融、運籌學和計算機科學專業的學生。它以有趣且有教育意義的例子和練習自然地呈現概率理論、定義、定理和方法。這本書在數學上嚴謹,同時與概率的歷史發展密切相關。在適當的時候,書中包含了歷史注解,並且2096個例子和練習都經過精心設計,以激發學生的好奇心,並鼓勵他們熱情地深入研究理論。

目錄大綱

1.Axioms of Probability
2.Combinatorial Methods
3.Conditional Probability and Independence
4.Distribution Functions and Discrete Random Variables
5.Special Discrete Distributions
6.Continuous Random Variables
7.Special Continuous Distributions
8.Bivariate Distributions
9.Multivariate Distributions
10.More Expectations and Variances
11.Sums of Independent Random Variables and Limit Theorems
12.Stochastic Processes

目錄大綱(中文翻譯)

1. 機率公理
2. 組合方法
3. 條件機率和獨立性
4. 分佈函數和離散隨機變量
5. 特殊離散分佈
6. 連續隨機變量
7. 特殊連續分佈
8. 雙變量分佈
9. 多變量分佈
10. 更多期望和變異數
11. 獨立隨機變量的和與極限定理
12. 隨機過程