Probability: Modeling and Applications to Random Processes (Hardcover)

Gregory K. Miller

  • 出版商: Wiley
  • 出版日期: 2006-08-01
  • 定價: $1,100
  • 售價: 9.5$1,045
  • 語言: 英文
  • 頁數: 488
  • 裝訂: Hardcover
  • ISBN: 0471458929
  • ISBN-13: 9780471458920
  • 相關分類: 機率統計學 Probability-and-statistics
  • 立即出貨 (庫存=1)

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Description

Improve Your Probability of Mastering This Topic

This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic models concurrent with the development of distribution theory while also introducing the reader to basic statistical inference. In this way, the major stochastic processes are blended with coverage of probability laws, random variables, and distribution theory, equipping the reader to be a true problem solver and critical thinker.

Deliberately conversational in tone, Probability is written for students in junior- or senior-level probability courses majoring in mathematics, statistics, computer science, or engineering. The book offers a lucid and mathematicallysound introduction to how probability is used to model random behavior in the natural world. The text contains the following chapters:
* Modeling
* Sets and Functions
* Probability Laws I: Building on the Axioms
* Probability Laws II: Results of Conditioning
* Random Variables and Stochastic Processes
* Discrete Random Variables and Applications in Stochastic Processes
* Continuous Random Variables and Applications in Stochastic Processes
* Covariance and Correlation Among Random Variables

Included exercises cover a wealth of additional concepts, such as conditional independence, Simpson's paradox, acceptance sampling, geometric probability, simulation, exponential families of distributions, Jensen's inequality, and many non-standard probability distributions.

 

Table of Contents

Preface.

To the Student.

To the Instructor.

Coverage.

Acknowledgments.

Chapter 1. Modeling.

1.1  Choice and Chance.

1.2  The Model Building Process.

1.3  Modeling in the Mathematical Sciences.

1.4  A First Look at a Probability Model: The Random Walk.

1.5  Brief Applications of Random Walks.

Exercises.

Chapter 2.  Sets and Functions.

2.1  Operations with Sets.

2.2  Functions.

2.3  The Probability Function and the Axioms of Probability.

2.4  Equally Likely Sample Spaces and Counting Rules.

Rules.

Exercises.

Chapter 3.  Probility Laws I: Building on the Axioms.

3.1  The Complement Rule.

3.2  The Addition Rule.

3.3  Extensions and Additional Results.

Exercises.

Chapter 4.  Probility Laws II: Results of Conditioning.

4.1  Conditional Probability and the Multiplication Rule.

4.2  Independent Events.

4.3  The Theorem of Total Probabilities and Bayes' Rule.

4.4  Problems of Special Interest: Effortful Illustrations of the Probability Laws.

Exercises.

Chapter 5.  Random Variables and  Stochastic Processes.

5.1  Roles and Types of Random Variables.

5.2  Expectation.

5.3  Roles, Types, and Characteristics of  Stochastic Processes.

Exercises.

Chapter 6.  Discrete Random Variables and Applications in Stochastic Processes.

6.1  The Bernoulli and Binomial Models.

6.2  The Hypergeometric Model.

6.3  The Poisson Model.

6.4  The Geometric and Negative Binomial.

Models.

Exercises.

Chapter 7.  Continuous Random Variables and Applications in Stochastic Processes.

7.1  The Continuous Uniform Model.

7.2  The Exponential Model.

7.3  The Gamma Model.

7.4  The Normal Model.

Chapter 8.  Covariance and Correlation Among Random Variables.

8.1  Joint, Marginal and Conditional Distributions.

8.2  Covariance and Correlation.

8.3  Brief  Examples and Illustrations in Stochastic Processes and Times Series.

Exercises.

Bibliography.

Tables.

Index.

商品描述(中文翻譯)

描述

這本書以創建隨機現象模型的框架為基礎,採用創新的方法來提高基於微積分的概率理論的掌握機會。作者專注於在發展分佈理論的同時合成隨機模型,同時介紹讀者基本的統計推斷。通過這種方式,主要的隨機過程與概率法則、隨機變量和分佈理論相結合,使讀者成為真正的問題解決者和批判性思考者。

《概率》以對話的方式撰寫,針對數學、統計、計算機科學或工程專業的大三或大四學生。本書提供了一個清晰且數學上可靠的介紹,說明了概率如何用於模擬自然界中的隨機行為。本書包含以下章節:

* 模型
* 集合和函數
* 概率法則 I:基於公理的建立
* 概率法則 II:條件概率的結果
* 隨機變量和隨機過程
* 離散隨機變量及其在隨機過程中的應用
* 連續隨機變量及其在隨機過程中的應用
* 隨機變量之間的協方差和相關性

附帶的練習涵蓋了許多其他概念,例如條件獨立性、辛普森悖論、接受抽樣、幾何概率、模擬、指數分佈族、詹森不等式以及許多非標準概率分佈。

目錄

前言
給學生的話
給教師的話
內容
致謝
第一章 模型
1.1 選擇和機會
1.2 模型建立過程
1.3 數學科學中的建模
1.4 概率模型的首次觀察:隨機遊走
1.5 隨機遊走的簡要應用
練習
第二章 集合和函數
2.1 集合的運算
2.2 函數
2.3 概率函數和概率公理
2.4 等可能樣本空間和計數規則
規則
練習
第三章 概率法則 I:基於公理的建立
3.1 互補規則
3.2 加法規則
3.3 擴展和其他結果
練習
第四章 概率法則 II:條件概率的結果
4.1 條件概率和乘法規則
4.2 獨立事件
4.3 總概率定理和貝葉斯定理
4.4 特殊問題:概率法則的努力說明
練習
第五章 隨機變量和隨機過程
5.1 隨機變量的角色和類型
5.2 期望值
5.3 隨機過程的角色、類型和特徵
練習
第六章 離散隨機變量及其在隨機過程中的應用
6.1 伯努利和二項模型
6.2 超幾何模型
6.3 泊松模型