《概率论与数理统计》(全英语)教学大纲课程名称概率

《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（MorrisH.DeGroot），[美]舍维什（MarkJ.Schervish）著MorrisH.DeGroot，MarkJ.Schervish编,机械工业出版社,2012教学参考:[1]M.N.DeGroot,M.J.Schervish,ProbabilityandStatistics,3rded.Boston,MA;London:Addison-Wesley,2002[2]Jay.L.Devore,ProbabilityandStatistics,5thed.HigherEducationPress,2010[3]H.Jeffreys,TheoryofProbability,3rded.Oxford:OxfordUniversityPress,1998[4]J.T.McClave,T.Sincich,AFirstCourseinStatistics,7thed.UpperSaddleRiver,NJ:PrenticeHall;London:Prentice-HallInternational,2000[5]S.M.Ross,IntroductiontoProbabilityandStatisticsforEngineersandScientists,2nded.SanDiego,CA;London:Harcourt/Academic,2000[6]V.K.Rothagi,S.M.Ehsanes,AnIntroductiontoProbabilityandStatistics,2nded.NewYork,Chichester:Wiley,2001ProbabilityandStatistics(English)CurriculumIntroductionCourseTitle:ProbabilityandStatistics(English)TotalHours:48Credit:2.5Pre-Course：Calculus,LinearAlgebraDepartmentofgivingcourse:DepartmentofmathematicsinShanghaiJiaotongUniveristyTextbook:ProbabilityandStatistics(fourthedition),[美]德格鲁特（MorrisH.DeGroot），[美]舍维什（MarkJ.Schervish）著MorrisH.DeGroot，MarkJ.Schervish编,机械工业出版社,2012Reference:[1]M.N.DeGroot,M.J.Schervish,ProbabilityandStatistics,3rded.Boston,MA;London:Addison-Wesley,2002[2]Jay.L.Devore,ProbabilityandStatistics,5thed.HigherEducationPress,2010[3]H.Jeffreys,TheoryofProbability,3rded.Oxford:OxfordUniversityPress,1998[4]J.T.McClave,T.Sincich,AFirstCourseinStatistics,7thed.UpperSaddleRiver,NJ:PrenticeHall;London:Prentice-HallInternational,2000[5]S.M.Ross,IntroductiontoProbabilityandStatisticsforEngineersandScientists,2nded.SanDiego,CA;London:Harcourt/Academic,2000[6]V.K.Rothagi,S.M.Ehsanes,AnIntroductiontoProbabilityandStatistics,2nded.NewYork,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。Probabilityandstatisticsisamathematicaldisciplinewhichstudiesstochasticphenomena.Nowitiswidelyusedinindustrialandagriculturalproduction,scienceandtechnologies.Thiscourseisoneoftheimportantbasiccoursesforengineeringmajorsincomprehensiveuniversities,throughwhichstudentsshallknowthegeneralconceptionsandmethodsaboutprobabilityandstatistics,masterthebasicdefinitions,theoriesandcorrespondingmethods,masterthemethodstodealwithrandomphenomenonbymeansofestablishingthebasicstatisticalmodelsandmasterthenecessaryabilityinEnglishlistening,speakingandsoon.Westresstheoryandpracticecombined,inordertohelpstudentspromotetheirabilityofapplyingstatisticalmethodsintheirdailylifeandscientificresearch.教学大纲及其教学要求ContentsofEachChapter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。Chapter1.Randomeventsandprobability(4hours)[Abstract]Theconceptofrandomevents,therelationshipbetweeneventsandcalculationsrelated.Thecalculationlawsforprobabilities.[TeachingRequirements]1.Understandtheconceptsofrandomeventsandsamplespace.Mastertherelationshipofeventsandrelatedcalculations.Understandthedefinitions,propertiesandlawsofunion,intersection,differenceandcomplementoperationsofrandomevents.2.Understandthestatisticaldefinitionofprobability.Mastertherelationshipbetweenfrequencyandprobability.Usethedefinitionsandcalculationformulas(beawareoftheirdifference)tosolveclassicalprobabilitymodelsandgeometricprobabilitymodels.Masterthemethodstosolvesomeelementaryprobabilityproblems.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。Chapter2.Conditionalprobability(4hours)[Abstract]Theconceptandthepropertiesofconditionalprobability.Methodstosolveprobabilityproblemsbymultiplicationrule,totalprobabilityformulaandBayes'Rule.Theconceptofindependentevents.Methodstosolveprobabilityproblemsbytheindependenceoftheevents.[TeachingRequirements]1.Understandtheconceptandthepropertiesofconditionalprobability.2.Masterthemethodstosolveprobabilityproblemsbymultiplicationrule,totalprobabilityformulaandBayes'Rule.3.Understandtheconceptofindependentevents,masterthemethodstosolveprobabilityproblemsbytheindependenceoftheevents.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，掌握它们的定义、性质及相关计算。Chapter3.Randomvariablesandtheirdistributions(8hours)[Abstract]Theconceptofone-dimensionalrandomvariables.Theconceptandpropertiesofthecumulativedistributionofrandomvariables.Someimportantdistributionsofdiscreteandcontinuousrandomvariables.Thedistributionsoffunctionsofarandomvariable.[TeachingRequirements]1.Thedefinitionofone-dimensionalrandomvariablesandtheirdistributions.2.Understandthedefinition