The Probability Lifesaver: All the Tools You Need to Understand Chance

The Probability Lifesaver: All the Tools You Need to Understand Chance (Princeton Lifesaver Study Guides)
by Steven Miller
Pages: 752 pages
Publisher finelybook 出版社:‏ Princeton University Press (14 Jun. 2017)
Language 语言: English
ISBN-10: 0691149542
ISBN-13: 9780691149547
B01N8U6YNU
The essential lifesaver for students who want to master probability
For students learning probability,its numerous applications,techniques,and methods can seem intimidating and overwhelming. That’s where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course,this accessible and user-friendly study guide helps students comfortably navigate probability’s terrain and achieve positive results.
The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University,Mount Holyoke College,and Williams College. With a relaxed and informal style,Miller presents the math with thorough reviews of prerequisite materials,worked-out problems of varying difficulty,and proofs. He explores a topic first to build intuition,and only after that does he dive into technical details. Coverage of topics is comprehensive,and materials are repeated for reinforcement—both in the guide and on the book’s website. An appendix goes over proof techniques,and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus.
The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses.
A helpful introduction to probability or a perfect supplement for a course
Numerous worked-out examples
Lectures based on the chapters are available free online
Intuition of problems emphasized first,then technical proofs given
Appendixes review proof techniques
Relaxed,conversational approach
Contents
Part I General Theory
Chapter 1 Introduction
Chapter 2 Basic Probability Laws
Chapter 3 Counting I: Cards
Chapter 4 Conditional Probability,Independence,And Bayes’ Theorem
Chapter 5 Counting Ii: Inclusion-Exclusion
Chapter 6 Counting Iii: Advanced Combinatorics
Part II Introduction To Random Variables
Chapter 7 Introduction To Discrete Random Variables
Chapter 8 Introduction To Continuous Random Variables
Chapter 9 Tools: Expectation
Chapter 10 Tools: Convolutions And Changing Variables
Chapter 11 Tools: Differentiating Identities
Part III Special Distributions
Chapter 12 Discrete Distributions
Chapter 13 Continuous Random Variables: Uniform And Exponential
Chapter 14 Continuous Random Variables: The Normal Distribution
Chapter 15 The Gamma Function And Related Distributions
Chapter 16 The Chi-Square Distribution
Part IV Limit Theorems
Chapter 17 Inequalities And Laws Of Large Numbers
Chapter 18 Stirling’S Formula
Chapter 19 Generating Functions And Convolutions
Chapter 20 Proof Of The Central Limit Theorem
Chapter 21 Fourier Analysis And The Central Limit Theorem
Part V Additional Topics
Chapter 22 Hypothesis Testing
Chapter 23 Difference Equations,Markov Processes,And Probability
Chapter 24 The Method Of Least Squares
Chapter 25 Two Famous Problems And Some Coding
Appendix A Proof Techniques
Appendix B Analysis Results
Appendix C Countable and Uncountable Sets
Appendix D Complex Analysis and the Central Limit Theorem
想要掌握概率的学生的基本救生员
对于学生的学习概率，它的众多应用，技术和方法看起来可以吓倒和压倒一切。这就是概率救生员进入的地方。旨在作为课程的完整独立介绍或作为课程的补充，这种易于访问和用户友好的学习指南有助于学生舒适地浏览概率的地形并取得积极成果。
概率救生员基于Steven Miller在布朗大学，霍尼克斯学院和威廉姆斯学院任教的成功课程。随着轻松和非正式的风格，米勒提供了对前提材料的彻底审查，不同难度的解决问题和证明的数学。他首先探讨一个话题来建立直觉，只有在此之后，他才能深入了解技术细节。主题的涵盖范围是全面的，材料重复加强，无论是在指南和书籍的网站上。附录超过了验证技术，课程的视频讲座可以在线获得。使用本书的学生应该熟悉代数和预先计算。
概率救生员不仅使学生能够生存概率，而且还能够掌握未来课程中使用的主题。
有助于介绍概率或完美补充课程
大量的例子
基于这些章节的讲座可免费上网
直觉问题首先强调，然后给出技术证明
附录审查证明技术
放松，对话的方法
目录
第一部分一般理论
第一章介绍
第二章基本概率法
第3章计数我: 卡
第四章条件概率，独立性和贝叶斯定理
第5章计数Ii: 包容排除
第六章计数Iii: 高级组合
第二部分随机变量简介
第7章离散随机变量简介
第8章连续随机变量简介
第9章工具: 期待
第10章工具: 卷积和变化变量
第11章工具: 区分身份
第三部分特刊
第12章离散分布
第13章连续随机变量: 均匀和指数
第14章连续随机变量: 正态分布
第15章伽玛函数及相关分布
第16章卡方分布
第四部分极限定理
第十七章大数的不平等与法律
第18章斯特林的公式
第19章生成函数和卷积
第20章中心极限定理的证明
第21章傅里叶分析与中心极限定理
第五部分附加主题
第22章假设检验
差异方程，马尔可夫过程和概率
第24章最小二乘法
第25章两个着名问题和一些编码
附录A证明技术
附录B分析结果
附录C可数和不可数集
附录D综合分析和中心极限定理
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