《概率论与数理统计》（全英语）教学大纲 课程名称：概率论与数理统计 学时：48学时 学分：2.5分 先修课程：高等数学，线性代数 开课院系：上海交通大学理学院数学系 教材：华章统计学原版精品系列：概率统计（英文版第4版），[美] 德格鲁特(Morris H.DeGroot),[美]舍维什(Mark J.Schervish)著 Morris H.DeGroot,Mark J.Schervish编，机械工业出版社，20l2 教学参考： [M.N.DeGroot,MJ.Schervish,Probability and Statistics,3rd ed.Boston,MA:London: Addison-Wesley,2002 [2]Jay.L Devore,Probability and Statistics,5th ed.Higher Education Press,2010 ,1998 Hall;London:Prentice-Hall International,2000 [5]S.M.Ross,Introduction to Probability and Statistics for Engineers and Scientists,2nd ed.San Diego,CA;London:Harcourt/Academic,2000 [6]V.K.Rothagi,S.M.Ehsanes,An Introduction to Probability and Statistics,2nd ed. New York,Chichester:Wiley,2001 Probability and Statistics(English) Curriculum Introduction Course Title:Probability and Statistics(English) Total Hours:48 Credit:2.5 Pre-Course:Calculus,Linear Algebra Department of giving course:Department of mathematics in Shanghai Jiaotong Univeristy Textbook:Probability and Statistics fourth edition),Morris H.DeGroot Mark J.Schervish,China Machine Press,2012
《概率论与数理统计》(全英语)教学大纲 课程名称: 概率论与数理统计 学时:48 学时 学分:2.5 分 先修课程:高等数学,线性代数 开课院系:上海交通大学理学院数学系 教材: 华章统计学原版精品系列：概率统计（英文版·第 4 版）, [美] 德格鲁特 （Morris H.DeGroot），[美]舍维什 （Mark J.Schervish） 著 Morris H.DeGroot ，Mark J.Schervish 编 , 机械工业出版社, 2012 教学参考: [1] M.N. DeGroot, M.J. Schervish, Probability and Statistics, 3rd ed. Boston, MA; London: Addison-Wesley, 2002 [2] Jay.L. Devore, Probability and Statistics, 5th ed. Higher Education Press, 2010 [3] H. Jeffreys, Theory of Probability, 3rd ed. Oxford: Oxford University Press, 1998 [4] J.T. McClave, T. Sincich, A First Course in Statistics, 7th ed. Upper Saddle River, NJ: Prentice Hall; London: Prentice-Hall International, 2000 [5]S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists,2nd ed. San Diego, CA; London: Harcourt/Academic, 2000 [6] V.K. Rothagi, S.M. Ehsanes, An Introduction to Probability and Statistics, 2nd ed. New York, Chichester: Wiley, 2001 Probability and Statistics (English) Curriculum Introduction Course Title: Probability and Statistics (English) Total Hours: 48 Credit: 2.5 Pre-Course：Calculus, Linear Algebra Department of giving course: Department of mathematics in Shanghai Jiaotong Univeristy Textbook: Probability and Statistics ( fourth edition), Morris H.DeGroot ，Mark J.Schervish, China Machine Press, 2012
Reference [MN.DeGroot,MJ.Schervish,Probability and Statistics,3rd ed.Boston,MA ondon:Addison-Wesley,2002 2 Jav.L.Devore.Probability and Statistics,5th ed.Higher Education Press,2010 [3]H.Jeffreys,Theory of Probability,3rd ed.Oxford:Oxford University Press,1998 [4]J.T.MeClave,T.Sincich,A First Course in Statistics,7th ed.Upper Saddle River. NJ:Prentice Hall;London:Prentice-Hall International,2000 [5]S.M.Ross,Introduction to Probability and Statistics for Engineers and Scientists,2nd ed.San Diego,CA;London:Harcourt/Academic,2000 [6]V.K.Rothagi,S.M.Ehsanes,An Introduction to Probability and Statistics,2nd ed. New York,Chichester:Wiley,2001 <概率论与数理统计>>是一门从数量方面研究随机现象规律性 的数学学科，它已广泛地应用于工农业生产和科学技术之中，并与其 它数学分支互相渗透与结合。本课程是工科类专业的一门重要公共基 础课程，并且是一门理论背景和应用性都很强的课程。本课程是全英 语教学，学生通过本课程的学习，在掌握处理随机现象的基本思想 和方法，培养学生运用概率与数理统计的方法去分析和解决实际问题 能力的基础上，学生还能掌握本课程专业英语的听、读和写，提升学 术应用和国际学术交流能力，为今后在国内外学习后继课程打下必需 的基础。 Probability and statistics is a mathematical discipline which studies stochastic phenomena.Now it is widely used in industrial and agricultural production,science majors in comprehensive universities,through which students shall know the genera conceptions and methods about probability and statistics,master the basic definitions. theories and corresponding methods,master the methods to deal with random phenomenon by means of establishing the basic statistical models and master the y aomy gsn stcnng,speaking and so on.We stress theory and practice order to help their ability of applying statistical methods in their daily life and scientific research
Reference: [1] M.N. DeGroot, M.J. Schervish, Probability and Statistics, 3rd ed. Boston, MA; London: Addison-Wesley, 2002 [2] Jay.L. Devore, Probability and Statistics, 5th ed. Higher Education Press, 2010 [3] H. Jeffreys, Theory of Probability, 3rd ed. Oxford: Oxford University Press, 1998 [4] J.T. McClave, T. Sincich, A First Course in Statistics, 7th ed. Upper Saddle River, NJ: Prentice Hall; London: Prentice-Hall International, 2000 [5] S.M. Ross, Introduction to Probability and Statistics for Engineers and Scientists,2nd ed. San Diego, CA; London: Harcourt/Academic, 2000 [6] V.K. Rothagi, S.M. Ehsanes, An Introduction to Probability and Statistics, 2nd ed. New York, Chichester: Wiley, 2001 <<概率论与数理统计>>是一门从数量方面研究随机现象规律性 的数学学科，它已广泛地应用于工农业生产和科学技术之中，并与其 它数学分支互相渗透与结合。本课程是工科类专业的一门重要公共基 础课程，并且是一门理论背景和应用性都很强的课程。本课程是全英 语教学， 学生通过本课程的学习，在掌握处理随机现象的基本思想 和方法，培养学生运用概率与数理统计的方法去分析和解决实际问题 能力的基础上，学生还能掌握本课程专业英语的听、读和写，提升学 术应用和国际学术交流能力，为今后在国内外学习后继课程打下必需 的基础。 Probability and statistics is a mathematical discipline which studies stochastic phenomena. Now it is widely used in industrial and agricultural production, science and technologies. This course is one of the important basic courses for engineering majors in comprehensive universities, through which students shall know the general conceptions and methods about probability and statistics, master the basic definitions, theories and corresponding methods, master the methods to deal with random phenomenon by means of establishing the basic statistical models and master the necessary ability in English listening, speaking and so on. We stress theory and practice combined, in order to help students promote their ability of applying statistical methods in their daily life and scientific research
教学大纲及其教学要求 Contents of Each Chapter 第一章随机事件和概率(4学时) [内容要点] 事件及事件间的关系及运算。概率的运算法则，计算随机事件的概率。 [教学要求] 1.理解随机事件和样本空间，熟悉事件的关系和性质，了解事件的并， 交，差和余的定义及运算法则。 2.了解概率的统计定义及频率与概率的关系，掌握古典概型和几何概型 的定义及计算公式，了解它们的异同，会计算一些初等的概率 Chapter 1.Random events and probability(4 hours) [Abstract] The concept of random events,the relationship between events and calculations related.The calculation laws for probabilities. [Teaching Requ ements] .Understand the oncepts of random events and sample space.Master the relationship of events and related calculations.Understand the definitions, properties and laws of union,intersection,difference and complement operations of random events. 2.Understand the statistical definition of probability.Master the relationship between frequency and probability.Use the definitions and calculati formulas(be aware of their difference)to solve classical probability models and geometric probability models.Master the methods to solve some elementary probability problems. 第二章条件概率(4学时) 内容要点 条件概率的定义及其性质，掌握运用乘法公式，全概率公式和贝 叶斯公式的概率计算。事件独立性的概念，运用事件的独立性的概率计算
教学大纲及其教学要求 Contents of Each Chapter 第一章 随机事件和概率 (4 学时) [内容要点] 事件及事件间的关系及运算。概率的运算法则，计算随机事件的概率。 [教学要求] 1．理解随机事件和样本空间，熟悉事件的关系和性质，了解事件的并， 交，差和余的定义及运算法则。 2．了解概率的统计定义及频率与概率的关系，掌握古典概型和几何概型 的定义及计算公式，了解它们的异同，会计算一些初等的概率。 Chapter 1. Random events and probability (4 hours) [Abstract] The concept of random events, the relationship between events and calculations related. The calculation laws for probabilities. [Teaching Requirements] 1. Understand the concepts of random events and sample space. Master the relationship of events and related calculations. Understand the definitions, properties and laws of union, intersection, difference and complement operations of random events. 2. Understand the statistical definition of probability. Master the relationship between frequency and probability. Use the definitions and calculation formulas (be aware of their difference) to solve classical probability models and geometric probability models. Master the methods to solve some elementary probability problems. 第二章 条件概率 (4 学时) [内容要点] 条件概率的定义及其性质，掌握运用乘法公式，全概率公式和贝 叶斯公式的概率计算。事件独立性的概念，运用事件的独立性的概率计算
[教学要求] 1.掌握条件概率的定义及其性质。 2.熟练应用全概率公式和Bayes公式进行概率计算。 3.掌握事件独立性的概念，熟练运用事件的独立性进行概率计算。 Chapter 2.Conditional probability(4 hours) [Abstract] The concept and the properties of conditional probability.Methods to solve probability Bayes Rule problems total probability formula and The concep of too probability problems by the independence of the events. [Teaching Requirements] 1.Understand the concept and the properties of conditional probability. 2.Master the methods to solve probability problems by multiplication rule. total probability formula and Bayes'Rule. 3.Underst nd the concept of independent events,master the methods to solve probability problems by the independence of the events. 第三章随机变量及其分布（⑧学时） 内容要点 一维随机变量，几个重要的分布。随机变量的分布函数及其性质，几个重 要的离散型和连续型分布。一维随机变量函数的分布。 教学要求] 1.理解随机变量的概念及分类。 2.掌握一维离散型随机变量的定义及其分布列，掌握一维离散型随机变量 函数的分布列的求法。 3.掌握连续型随机变量的定义，密度函数的定义和性质。掌握一维连续型 随机变量分布函数的定义和性质。掌握一维连续性随机变量函数分布的 求法。 4.熟悉常用分布，二项分布，泊松分布，几何分布，巴斯卡分布，均匀分
[教学要求] 1. 掌握条件概率的定义及其性质。 2 . 熟练应用全概率公式和 Bayes 公式进行概率计算。 3．掌握事件独立性的概念，熟练运用事件的独立性进行概率计算。 Chapter 2. Conditional probability (4 hours) [Abstract] The concept and the properties of conditional probability. Methods to solve probability problems by multiplication rule, total probability formula and Bayes' Rule. The concept of independent events. Methods to solve probability problems by the independence of the events. [Teaching Requirements] 1. Understand the concept and the properties of conditional probability. 2. Master the methods to solve probability problems by multiplication rule, total probability formula and Bayes' Rule. 3. Understand the concept of independent events, master the methods to solve probability problems by the independence of the events. 第三章 随机变量及其分布 (8 学时) [内容要点] 一维随机变量，几个重要的分布。随机变量的分布函数及其性质，几个重 要的离散型和连续型分布。一维随机变量函数的分布。 [教学要求] 1．理解随机变量的概念及分类。 2. 掌握一维离散型随机变量的定义及其分布列，掌握一维离散型随机变量 函数的分布列的求法。 3. 掌握连续型随机变量的定义，密度函数的定义和性质。掌握一维连续型 随机变量分布函数的定义和性质。掌握一维连续性随机变量函数分布的 求法。 4. 熟悉常用分布，二项分布，泊松分布，几何分布，巴斯卡分布，均匀分
布，指数分布，特别是正态分布，学握它们的定义、性质及相关计算。 Chapter 3.Random variables and their distributions(8 hours) [Abstract] The concept of one-dimensional random variables.The concept and properties of the cumulative distribution of random variables. Some sibutions of discrete and continuous random variables.The of functions of a random variable [Teaching Requirements] 1.The definition of one-dimensional random variables and their distributions 2.Understand the definition and distribution of discrete random variables. Master the methods to solve the distribution of the function of one discrete random variables finition and distribution of continuous random variable Understand the definition and properties of probability density function(pdf) of continuous random variables.Understand the definition and properties of functions of continuous random variables.Master the methods to solve the distribution of the function of one continuous random variable. 4.Master the definitions characteristics propertie and calculations of used,like Binomial Distribution Poissn Distribution Geometric Distribution,Pascal Distribution,Uniform Distribution, Exponential Distribution,and most importantly,Normal Distribution. 第四章多维随机变量(6学时) 「内容要点] 多维随机变量。二维随机变量及其联合分布与边缘分布的关系，条件分布。 二维随机变量函数的分布。多维随机变量及其联合分布与边缘分布的关 系。随机变量的独立性，相互独立的随机变量函数的概率计算。 [教学要求] 1.掌握多维随机变量的概念，理解二维随机变量的联合分布，边缘分布， 会求简单的二维随机问题的联合分布和边缘分布。 2.了解二维随机变量的条件分布，理解离散型随机变量的条件分布率及连 续性随机变量的条件分布和条件分布密度函数，及它们的计算公式
布，指数分布，特别是正态分布，掌握它们的定义、性质及相关计算。 Chapter 3. Random variables and their distributions (8 hours) [Abstract] The concept of one-dimensional random variables. The concept and properties of the cumulative distribution of random variables. Some important distributions of discrete and continuous random variables. The distributions of functions of a random variable. [Teaching Requirements] 1. The definition of one-dimensional random variables and their distributions. 2. Understand the definition and distribution of discrete random variables. Master the methods to solve the distribution of the function of one discrete random variables. 3. Understand the definition and distribution of continuous random variables. Understand the definition and properties of probability density function (pdf) of continuous random variables. Understand the definition and properties of functions of continuous random variables. Master the methods to solve the distribution of the function of one continuous random variable. 4. Master the definitions, characteristics properties and calculations of distributions frequently used, like Binomial Distribution, Poisson Distribution, Geometric Distribution, Pascal Distribution, Uniform Distribution, Exponential Distribution, and most importantly, Normal Distribution. 第四章 多维随机变量(6 学时) [内容要点] 多维随机变量。二维随机变量及其联合分布与边缘分布的关系，条件分布。 二维随机变量函数的分布。多维随机变量及其联合分布与边缘分布的关 系。随机变量的独立性，相互独立的随机变量函数的概率计算。 [教学要求] 1．掌握多维随机变量的概念，理解二维随机变量的联合分布，边缘分布， 会求简单的二维随机问题的联合分布和边缘分布。 2. 了解二维随机变量的条件分布，理解离散型随机变量的条件分布率及连 续性随机变量的条件分布和条件分布密度函数，及它们的计算公式