东北大学：某学院应用统计学专业《概率论与随机变量》课程教学大纲

概率论与随机变量教学大纲Probability and RandomSubject SyllabusVariables一、课程信息SubjectInformation课程编号：开课学期：3310031200Subject IDSemester课程分类：所属课群：专业方向类SectionCategory课程学分总学时/周：3.556Credit PointsTotal Hours/Weeks理论学时：实验学时：560LECT. HoursEXP. HoursPBL学时：实践学时/周：00PBL HoursPRAC.Hours/Weeks东北大学秦皇岛分开课学院适用专业：校应用统计学ASCollegeStream悉尼智能科技学院课程属性课程模式：引进UTS必修CompulsoryPatternMode中方课程协调人：Gui-Lai Zhang成绩记载方式：百分制Marks张贵来NEU CoordinatorResult Type先修课程：数学分析与建模、线性代数RequisitesMathematicalAnalysisandModeling、LinearAlgebra英文参考教材Probability An Introduction,Geffrey Grimmett Dominic WelshENTextbooksOxford,2014中文参考教材概率论与数理统计（第4版）邓集贤等，高等教育出版社，2009CN Textbooks（上下两册）概率论基础（第2版）李贤平，高等教育出版社，2010教学资源：Probability and Statistics for Engineering and the Sciences.(NinthResourcesEdition)Jay L.Devore,2014张贵来提交日期：单击或点击此处输课程负责人(撰写人)：Subject DirectorGui-Lai ZhangSubmitted Date入日期。任课教师(含负责人):Stephen Woodcock,Gui-Lai ZhangTaught by审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：单击或点击此处输入日期。Approved Date1 / 12

1 / 12 概率论与随机变量 教学大纲 Subject Syllabus Probability and Random Variables 一、课程信息 Subject Information 课程编号: Subject ID 310031200 开课学期: Semester 3 课程分类: Category 所属课群: Section 专业方向类 课程学分: Credit Points 3.5 总学时/周: Total Hours/Weeks 56 理论学时: LECT. Hours 56 实验学时: EXP. Hours 0 PBL 学时: PBL Hours 0 实践学时/周: PRAC. Hours/Weeks 0 开课学院: College 东北大学秦皇岛分 校 悉尼智能科技学院 适用专业: Stream 应用统计学 AS 课程属性: Pattern 必修 Compulsory 课程模式: Mode 引进 UTS 中方课程协调人: NEU Coordinator Gui-Lai Zhang 张贵来 成绩记载方式: Result Type 百分制 Marks 先修课程: Requisites 数学分析与建模、线性代数 Mathematical Analysis and Modeling、Linear Algebra 英文参考教材: EN Textbooks Probability An Introduction，Geffrey Grimmett, Dominic Welsh, Oxford, 2014 中文参考教材: CN Textbooks 概率论与数理统计. （第 4 版） 邓集贤等，高等教育出版社，2009 （上下两册） 教学资源: Resources 概率论基础.（第 2 版） 李贤平，高等教育出版社，2010 Probability and Statistics for Engineering and the Sciences. (Ninth Edition) Jay L. Devore, 2014 课程负责人(撰写人): Subject Director 张贵来 Gui-Lai Zhang 提交日期: Submitted Date 单击或点击此处输 入日期。 任课教师(含负责人): Taught by Stephen Woodcock, Gui-Lai Zhang 审核人: Checked by 韩鹏 批准人: Approved by 史闻博 批准日期: Approved Date 单击或点击此处输 入日期

二、教学目标SubjectLearningObjectives(SLOs)注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject在对现实世界的问题建模时，我们需要处理不确定性，而概率提供了一种量化和建模不确定性的有效方法。本课程介绍了概率的概念，如依赖事件和独立事件以及条件概率。介绍了随机事件的分布建模思想，包括概率计算、期望、方差、生成函数和独立事件的顺序统计。最后讨论了离散马尔可夫链。Whenmodellingreal-worldproblems we needto deal with整体目标：uncertainty,and probability providesan effective wayto quantifyandOverall Objectivemodel uncertainty.This subjectintroduces concepts inprobability suchas dependent and independent events as well as conditional probabilityThe idea of modelling random events with distributions is introducedincluding probability calculation, expectation, variance, generatingfunctions, and order statistics for independent events. The subjectconcludesbyconsidering discrete Markovchains了解确定性与随机系统、隐藏状态模型、信号解释Recognize deterministic versus stochastic system,理解随机实验、概率的解释、韦恩图Understand random experiments, interpretations of probability1-1and Venn diagrams掌握条件概率、互斥、简单集理论和德摩根定律、贝叶斯定理Master conditional probability,mutual exclusivity, simple settheory and de Morgam's laws, Bayes Theorem了解累积概率函数Recognize cumulative probabilityfunctions理解离散随机变量1-2Understand discrete random variables掌握概率质量函数、期望和方差（1）专业目标：Master probability mass functions, expectation and varianceProfessional Ability掌握金融期权的公平定价和基本博奔论1-3Masterfair pricing offinancial options and elementarygame theory掌握伯努利分布和二项式分布、卷积1-4Master Bernoulli and Binomial distributions, convolutions了解指数分布及其与泊松分布的关系Recognize exponential distribution and its relation to Poissordistribution1-5掌握条件分布和条件期望，随机变量的函数Master conditional distributions and conditional expectation,functionsof random variables掌握生成函数、随机变量的和1-6Master generating functions and sums of random variables了解马尔科夫链分类1-7Recognizeclassificationof MarkovChains2 / 12

2 / 12 二、教学目标 Subject Learning Objectives (SLOs) 注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数 Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject. 整体目标: Overall Objective 在对现实世界的问题建模时，我们需要处理不确定性，而概率 提供了一种量化和建模不确定性的有效方法。本课程介绍了概率的 概念，如依赖事件和独立事件以及条件概率。介绍了随机事件的分 布建模思想，包括概率计算、期望、方差、生成函数和独立事件的 顺序统计。最后讨论了离散马尔可夫链。 When modelling real-world problems we need to deal with uncertainty, and probability provides an effective way to quantify and model uncertainty. This subject introduces concepts in probability such as dependent and independent events as well as conditional probability. The idea of modelling random events with distributions is introduced, including probability calculation, expectation, variance, generating functions, and order statistics for independent events. The subject concludes by considering discrete Markov chains. （1）专业目标: Professional Ability 1-1 了解确定性与随机系统、隐藏状态模型、信号解释 Recognize deterministic versus stochastic system, 理解随机实验、概率的解释、韦恩图 Understand random experiments, interpretations of probability and Venn diagrams 掌握条件概率、互斥、简单集理论和德摩根定律、贝叶斯定 理 Master conditional probability, mutual exclusivity, simple set theory and de Morgam’s laws, Bayes Theorem. 1-2 了解累积概率函数 Recognize cumulative probability functions 理解离散随机变量 Understand discrete random variables 掌握概率质量函数、期望和方差 Master probability mass functions, expectation and variance 1-3 掌握金融期权的公平定价和基本博弈论 Master fair pricing of financial options and elementary game theory 1-4 掌握伯努利分布和二项式分布、卷积 Master Bernoulli and Binomial distributions, convolutions 1-5 了解指数分布及其与泊松分布的关系 Recognize exponential distribution and its relation to Poisson distribution 掌握条件分布和条件期望，随机变量的函数 Master conditional distributions and conditional expectation, functions of random variables 1-6 掌握生成函数、随机变量的和 Master generating functions and sums of random variables 1-7 了解马尔科夫链分类 Recognize classification of Markov Chains

掌握离散马尔科夫链、可约性，周期性、瞬态和吸收状态Master discrete Markov Chains ,Reducibility,periodicityrecurrent/transient/absorbingstates培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神2-1Cultivate the spirit of not fearing difficulties or failure,perseverance,daring to try,and cultivate their own careful andpatient courage and spirit in the process of learning培养遵守法律、懂规则、守规则的新时代公民2-2Cultivate citizens of the new era who abide by the law,understand andobeytherules了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾2-3andUnderstandthemaincontradictionsecondarycontradiction, seek truth from facts and grasp the maincontradictioninthefaceofcomplexproblems引导同学们加强团队精神的学习，真正体会到团队力量的强大。使学生意识到：个人的力量是有限的，只有个人投入到集体团队中，通过高效沟通、良好协作，才能激发出无限力量，实现自身价值。（2）德育目标：Guide the students to strengthen the study of team spirit, and2-4EssentialQualitytruly experience the strong team strength.Make students realizethat the strength of individuals is limited, only individuals intothe collective team, through efficient communication, goodcooperation, can stimulateinfinitepower,torealizetheirownvalue勉励同学们养成良好的行为习惯，无论学习还是做事都要有毅力有恒心，培养坚持不的优秀品质。2-5Encourage students to developgood behaviorhabits,no matterstudyorworktohaveperseveranceandperseverance,cultivateunremitting excellent quality.联系时政，增强学生勇于探索的创新精神、善于解决实际问题的能力。2-6Contact current politics, enhance students'innovative spirit toexplore,goodattheabilityof solvingpracticalproblems.明确事物的普遍联系性和事物是不断变化发展的唯物主义观点，提高学生正确认识问题、分析问题解决问题的能力。2-7Clarifythe general connection of things and things is thechanging materialist view, and improve students'ability tocorrectly understand, analyze and solve problems课程教学目标与毕业要求的对应关系MatrixofGA&SLO毕业要求GA指标点GAIndex教学目标SLOs3/12

3 / 12 掌握离散马尔科夫链、可约性, 周期性、瞬态和吸收状态 Master discrete Markov Chains , Reducibility, periodicity, recurrent/transient/absorbing states （2）德育目标: Essential Quality 2-1 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难 而上的精神，并在学习过程中培养自己的细心和耐心的勇气 和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 2-2 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 2-3 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求 是、抓住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 2-4 引导同学们加强团队精神的学习，真正体会到团队力量的强 大。使学生意识到：个人的力量是有限的，只有个人投入到 集体团队中，通过高效沟通、良好协作，才能激发出无限力 量，实现自身价值。 Guide the students to strengthen the study of team spirit, and truly experience the strong team strength.Make students realize that the strength of individuals is limited, only individuals into the collective team, through efficient communication, good cooperation, can stimulate infinite power, to realize their own value. 2-5 勉励同学们养成良好的行为习惯，无论学习还是做事都要有 毅力有恒心，培养坚持不懈的优秀品质。 Encourage students to develop good behavior habits, no matter study or work to have perseverance and perseverance, cultivate unremitting excellent quality. 2-6 联系时政，增强学生勇于探索的创新精神、善于解决实际问 题的能力。 Contact current politics, enhance students' innovative spirit to explore, good at the ability of solving practical problems. 2-7 明确事物的普遍联系性和事物是不断变化发展的唯物主义 观点，提高学生正确认识问题、分析问题解决问题的能力。 Clarify the general connection of things and things is the changing materialist view, and improve students' ability to correctly understand, analyze and solve problems. 课程教学目标与毕业要求的对应关系 Matrix of GA & SLOs 毕业要求 GA 指标点 GA Index 教学目标 SLOs

1-1：具有较强的演绎推理能力、准确计算能力、分析归纳能力、抽象思维能力，掌握数学、自然科学和相关专业知识，并使用其建立正确的数学、物理学等模型以解释复杂实际问题；1-l:Capable of deductive reasoningaccurate calculation,analysisandinduction and abstractthinkingEstablishingcorrectmathematical and physical models withthe professional knowledge ofmathematics, natural science, etc. tosolvecomplexpracticalproblems1、理学知识：具有扎实的1-1 到 1-71-2：掌握统计调查、统计数据处理、统数学基础，能够将数学、自计分析、计算机与统计软件使用等应用2-1、2-7然科学和专业知识用于解决统计学的基本理论、知识与方法，具备复杂实际问题。采集、处理、分析数据的能力，熟悉预研报告、可行性分析报告、研究方案等1.Science Knowledge: Apply文档的撰写规范knowledge of mathematics,1-2: Mastery the basic theories, knowledge natural science, fundamentalsand methods of applied statistics, such as andanengineeringstatistical investigation, statistical dataspecialization to the solutionprocessing, statistical analysis, and the ueofcomplexengineeringof computers and statistical software,problems.capable of data collecting, processing, andanalyzing, familiar with the writing normsof pre-research reports,feasibility analysisreports,andresearchplans:1-3：了解本专业涉及相关行业的发展趋势以及相关产业的运营模式，具备在本专业相关领域进行方案设计、技术创新的能力。1-3:Understanding the development andoperations of related industries in thismajor, capable of conducting programdesign and technological innovation inrelated fields of this major.2、问题分析：能够借助应2-1：能够借助应用统计学的基本原理、用统计学的基本原理、方法方法和手段，分析、识别、表达本专业和手段，识别、表达、并通相关的复杂实际问题；1-1 到 1-7过文献研究分析复杂实际2-1: Capable of analyzing, identifying and2-1到2-7问题，以获得有效结论。elaborating complex practical problems2.ProblemAnalysis:related to this major with the applying ofIdentify, formulate, researchthe basicprinciples ofApplied Statistics;4 / 12

4 / 12 1、理学知识：具有扎实的 数学基础，能够将数学、自 然科学和专业知识用于解决 复杂实际问题。 1. Science Knowledge: Apply knowledge of mathematics, natural science, fundamentals and an engineering specialization to the solution of complex engineering problems. 1-1：具有较强的演绎推理能力、准确 计算能力、分析归纳能力、抽象思维能 力，掌握数学、自然科学和相关专业知 识，并使用其建立正确的数学、物理学 等模型以解释复杂实际问题； 1-1: Capable of deductive reasoning, accurate calculation, analysis and induction and abstract thinking. Establishing correct mathematical and physical models with the professional knowledge of mathematics, natural science, etc. to solve complex practical problems; 1-1 到 1-7 2-1、2-7 1-2：掌握统计调查、统计数据处理、统 计分析、计算机与统计软件使用等应用 统计学的基本理论、知识与方法，具备 采集、处理、分析数据的能力，熟悉预 研报告、可行性分析报告、研究方案等 文档的撰写规范; 1-2: Mastery the basic theories, knowledge and methods of applied statistics, such as statistical investigation, statistical data processing, statistical analysis, and the use of computers and statistical software; capable of data collecting, processing, and analyzing; familiar with the writing norms of pre-research reports, feasibility analysis reports, and research plans; 1-3：了解本专业涉及相关行业的发展趋 势以及相关产业的运营模式，具备在本 专业相关领域进行方案设计、技术创新 的能力。 1-3: Understanding the development and operations of related industries in this major; capable of conducting program design and technological innovation in related fields of this major. 2、问题分析：能够借助应 用统计学的基本原理、方法 和手段，识别、表达、并通 过文献研究分析复杂实际 问题，以获得有效结论。 2. Problem Analysis: Identify, formulate, research 2-1：能够借助应用统计学的基本原理、 方法和手段，分析、识别、表达本专业 相关的复杂实际问题； 2-1: Capable of analyzing, identifying and elaborating complex practical problems related to this major with the applying of the basic principles of Applied Statistics; 1-1 到 1-7 2-1 到 2-7

literatureandanalyze2-2：能够借助应用统计学的基本原理、方法和手段，针对复杂实际问题设计针complexpractical problems对性的方案，并综合运用文献、科学理reachingsubstantiated论和技术手段予以解决。conclusionsfirstusing2-2:Capable of drawing onthe basicprinciples of mathematics andsciences.principles of applied statistics to designtargeted schemes for complex practicalproblems, and using literature, scientifictheories and technicalmeansto solvethem.三、教学内容Content(Topics)注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit(1)理论教学Lecture知识单元序号支撑教学目标11-1、2-1到2-5Knowledge Unit No.SLOs Supported知识单元名称随机事件与概率Unit TitleRandomeventsand probability随机实验Random experiments确定性与随机系统Deterministicversus stochasticsystems概率的解释Interpretationsof probability条件概率Conditional probability互斥知识点：Mutual exclusivity维恩图Knowledge DeliveryVenn diagrams简单集理论和德摩根定律Simple set theory and de Morgan's laws贝叶斯定理Bayes Theorem隐藏状态模型Hidden state models信号的解释Interpretation of signals确定性与随机系统了解：学习目标：Deterministic versus stochastic systems隐藏状态模型Learning ObjectivesRecognizeHidden state models5/12

5 / 12 literature and analyze complex practical problems reaching substantiated conclusions using first principles of mathematics and sciences. 2-2：能够借助应用统计学的基本原理、 方法和手段，针对复杂实际问题设计针 对性的方案，并综合运用文献、科学理 论和技术手段予以解决。 2-2: Capable of drawing on the basic principles of applied statistics to design targeted schemes for complex practical problems, and using literature, scientific theories and technical means to solve them. 三、教学内容 Content (Topics) 注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减 Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit (1) 理论教学 Lecture 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1、2-1 到 2-5 知识单元名称 Unit Title 随机事件与概率 Random events and probability 知识点: Knowledge Delivery 随机实验 Random experiments 确定性与随机系统 Deterministic versus stochastic systems 概率的解释 Interpretations of probability 条件概率 Conditional probability 互斥 Mutual exclusivity 维恩图 Venn diagrams 简单集理论和德摩根定律 Simple set theory and de Morgan’s laws 贝叶斯定理 Bayes Theorem 隐藏状态模型 Hidden state models 信号的解释 Interpretation of signals 学习目标: Learning Objectives 了解: Recognize 确定性与随机系统 Deterministic versus stochastic systems 隐藏状态模型 Hidden state models

信号的解释Interpretation of signals随机实验Random experiments理解：概率的解释UnderstandInterpretations of probability维恩图Venn diagrams条件概率Conditional probability互斥掌握：Mutual exclusivityMaster简单集理论和德摩根定律Simple set theory and de Morgan's laws贝叶斯定理Bayes Theorem培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神Cultivate the spirit of not fearing difficulties or failure,perseverancedaring to try,and cultivate their own careful and patient courage andspirit in the process of learning了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓住主要矛盾Understand themain contradiction and secondary contradiction, seektruth from facts and grasp the main contradiction in the face ofcomplexproblems培养遵守法律、懂规则、守规则的新时代公民Cultivatecitizens ofthe new era who abide by the law, understand and德育目标obey the rulesMoral Objectives引导同学们加强团队精神的学习，真正体会到团队力量的强大。使学生意识到：个人的力量是有限的，只有个人投入到集体团队中，通过高效沟通、良好协作，才能激发出无限力量，实现自身价值。Guide the students to strengthen the study of team spirit, and trulyexperience the strong team strength.Make students realize that thestrength of individuals is limited, only individuals into the collectiveteam,throughefficientcommunication,goodcooperation,canstimulate infinitepower,torealize theirownvalue勉励同学们养成良好的行为习惯，无论学习还是做事都要有毅力有恒心，培养坚持不懈的优秀品质。Encourage students to develop good behavior habits, no matter study orwork to have perseverance and perseverance, cultivate unremittingexcellent quality随机实验；概率的解释：条件概率：互斥：维恩图：简单集理论和重点：德摩根定律贝叶斯定理Key PointsRandom experiments; Interpretations of probability,Conditional6 / 12

6 / 12 信号的解释 Interpretation of signals 理解: Understand 随机实验 Random experiments 概率的解释 Interpretations of probability 维恩图 Venn diagrams 掌握: Master 条件概率 Conditional probability 互斥 Mutual exclusivity 简单集理论和德摩根定律 Simple set theory and de Morgan’s laws 贝叶斯定理 Bayes Theorem 德育目标 Moral Objectives 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而上的 精神，并在学习过程中培养自己的细心和耐心的勇气和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 了解主要矛盾和次要矛盾，在面对复杂问题的时候要实事求是、抓 住主要矛盾 Understand the main contradiction and secondary contradiction, seek truth from facts and grasp the main contradiction in the face of complex problems 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 引导同学们加强团队精神的学习，真正体会到团队力量的强大。使 学生意识到：个人的力量是有限的，只有个人投入到集体团队中， 通过高效沟通、良好协作，才能激发出无限力量，实现自身价值。 Guide the students to strengthen the study of team spirit, and truly experience the strong team strength.Make students realize that the strength of individuals is limited, only individuals into the collective team, through efficient communication, good cooperation, can stimulate infinite power, to realize their own value. 勉励同学们养成良好的行为习惯，无论学习还是做事都要有毅力有 恒心，培养坚持不懈的优秀品质。 Encourage students to develop good behavior habits, no matter study or work to have perseverance and perseverance, cultivate unremitting excellent quality. 重点: Key Points 随机实验；概率的解释；条件概率；互斥；维恩图；简单集理论和 德摩根定律；贝叶斯定理 Random experiments; Interpretations of probability; Conditional

probability, Mutual exclusivity, Venn diagrams; Simple set theory andde Morgan's laws; Bayes Theorem难点：条件概率；互斥：贝叶斯定理Focal PointsConditionalprobability,Mutualexclusivity,BayesTheorem支撑教学目标：知识单元序号21-2、2-5Knowledge Unit No.SLOs Supported离散随机变量：概率质量函数：累积概率函数；期望和方差知识单元名称Discreterandomvariables;Probabilitymassfunctions;CumulativeUnit Titleprobability functions; Expectation and variance离散随机变量Discrete random variables概率质量函数知识点：Probability mass functionsKnowledge Delivery累积概率函数Cumulative probability functions期望和方差Expectation and variance了解：累积概率函数RecognizeCumulativeprobabilityfunctions学习目标：理解：离散随机变量Learning ObjectivesUnderstandDiscrete random variables掌握：概率质量函数；期望和方差MasterProbability mass functions; Expectation and variance勉励同学们养成良好的行为习惯，无论学习还是做事都要有毅力有恒心，培养坚持不解的优秀品质。德育目标Encouragestudentstodevelopgood behaviorhabits,nomatterstudyorMoral Objectiveswork to have perseverance and perseverance, cultivate unremittingexcellent quality.重点：概率质量函数：期望和方差Key PointsProbability mass functions; Expectation and variance概率质量函数；累积概率函数；期望和方差难点：Probability mass functions; Cumulative probability functions; ExpectationFocal Pointsand variance知识单元序号支撑教学目标：31-5、2-3、2-6Knowledge Unit NoSLOs Supported应用包括金融期权的公平定价和基本博奔论知识单元名称Applications including fair pricing of financial options and elementary gameUnit Titletheory金融期权的公平定价知识点：Fair pricing of financial optionsKnowledge Delivery基本博奔论Elementary game theory学习目标：掌握：金融期权的公平定价7/12

7 / 12 probability; Mutual exclusivity; Venn diagrams; Simple set theory and de Morgan’s laws; Bayes Theorem 难点: Focal Points 条件概率；互斥；贝叶斯定理 Conditional probability; Mutual exclusivity; Bayes Theorem 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-2、2-5 知识单元名称 Unit Title 离散随机变量；概率质量函数；累积概率函数；期望和方差 Discrete random variables; Probability mass functions; Cumulative probability functions; Expectation and variance 知识点: Knowledge Delivery 离散随机变量 Discrete random variables 概率质量函数 Probability mass functions 累积概率函数 Cumulative probability functions 期望和方差 Expectation and variance 学习目标: Learning Objectives 了解: Recognize 累积概率函数 Cumulative probability functions 理解: Understand 离散随机变量 Discrete random variables 掌握: Master 概率质量函数；期望和方差 Probability mass functions; Expectation and variance 德育目标 Moral Objectives 勉励同学们养成良好的行为习惯，无论学习还是做事都要有毅力有 恒心，培养坚持不懈的优秀品质。 Encourage students to develop good behavior habits, no matter study or work to have perseverance and perseverance, cultivate unremitting excellent quality. 重点: Key Points 概率质量函数；期望和方差 Probability mass functions; Expectation and variance 难点: Focal Points 概率质量函数；累积概率函数；期望和方差 Probability mass functions; Cumulative probability functions; Expectation and variance 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-5、2-3、2-6 知识单元名称 Unit Title 应用包括金融期权的公平定价和基本博弈论 Applications including fair pricing of financial options and elementary game theory 知识点: Knowledge Delivery 金融期权的公平定价 Fair pricing of financial options 基本博弈论 Elementary game theory 学习目标: 掌握: 金融期权的公平定价

Learning ObjectivesMasterFair pricing offinancial options基本博奔论Elementary game theory培养遵守法律、懂规则、守规则的新时代公民Cultivate citizens of the new era who abide by the law,understand andobey the rules德育目标联系时政，增强学生勇于探索的创新精神、善于解决实际问题的能Moral Objectives力。Contact current politics, enhance students' innovative spirit to explore,good at the ability of solving practical problems.金融期权的公平定价重点：Fair pricing of financial optionsKey Points基本博奔论Elementary game theory难点：金融期权的公平定价和基本博奔论Focal PointsFair pricing of financial options and elementary game theory知识单元序号支撑教学目标：41-6, 2-6Knowledge Unit NoSLOs Supported知识单元名称伯努利分布和二项式分布：卷积Unit TitleBernoulliandBinomialdistributions;convolutions伯努利分布Bernoulli distributions知识点：二项式分布Knowledge DeliveryBinomial distributions卷积convolutions学习目标：掌握：伯努利分布和二项式分布：卷积Learning ObjectivesMasterBernoulli and Binomial distributions; convolutions联系时政，增强学生勇于探索的创新精神、善于解决实际问题的能德育目标力。Moral ObjectivesContact currentpolitics,enhance students'innovativespiritto exploregoodattheabilityof solvingpracticalproblems类的定义与对象的创建重点：Definitions of class and creations of objectsKey Points成员函数的调用Member functions and theirs calling难点：类的一些高级应用方法Focal PointsAdvanced methods about class知识单元序号支撑教学目标：51-5、2-4Knowledge Unit NoSLOs Supported指数分布及其与泊松分布的关系：条件分布和条件期望：随机变量知识单元名称的函数Unit TitleExponential distribution and its relation to Poisson distribution; Conditional8/12

8 / 12 Learning Objectives Master Fair pricing of financial options 基本博弈论 Elementary game theory 德育目标 Moral Objectives 培养遵守法律、懂规则、守规则的新时代公民 Cultivate citizens of the new era who abide by the law, understand and obey the rules 联系时政，增强学生勇于探索的创新精神、善于解决实际问题的能 力。 Contact current politics, enhance students' innovative spirit to explore, good at the ability of solving practical problems. 重点: Key Points 金融期权的公平定价 Fair pricing of financial options 基本博弈论 Elementary game theory 难点: Focal Points 金融期权的公平定价和基本博弈论 Fair pricing of financial options and elementary game theory 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-6，2-6 知识单元名称 Unit Title 伯努利分布和二项式分布；卷积 Bernoulli and Binomial distributions; convolutions 知识点: Knowledge Delivery 伯努利分布 Bernoulli distributions 二项式分布 Binomial distributions 卷积 convolutions 学习目标: Learning Objectives 掌握: Master 伯努利分布和二项式分布；卷积 Bernoulli and Binomial distributions; convolutions 德育目标 Moral Objectives 联系时政，增强学生勇于探索的创新精神、善于解决实际问题的能 力。 Contact current politics, enhance students' innovative spirit to explore, good at the ability of solving practical problems. 重点: Key Points 类的定义与对象的创建 Definitions of class and creations of objects 成员函数的调用 Member functions and theirs calling 难点: Focal Points 类的一些高级应用方法 Advanced methods about class 知识单元序号: Knowledge Unit No. 5 支撑教学目标: SLOs Supported 1-5、2-4 知识单元名称 Unit Title 指数分布及其与泊松分布的关系；条件分布和条件期望；随机变量 的函数 Exponential distribution and its relation to Poisson distribution; Conditional

distributionsandconditional expectation;Functionsofrandomvariables指数分布及其与泊松分布的关系Exponential distribution and its relation to Poisson distribution知识点：条件分布和条件期望Knowledge DeliveryConditional distributions and conditional expectation随机变量的函数Functions of random variables了解：指数分布及其与泊松分布的关系RecognizeCommon operations about directories and files学习目标：条件分布和条件期望掌握：Learning ObjectivesConditional distributions and conditional expectationMaster随机变量的函数Functions of random variables引导同学们加强团队精神的学习，真正体会到团队力量的强大。使学生意识到：个人的力量是有限的，只有个人投入到集体团队中，通过高效沟通、良好协作，才能激发出无限力量，实现自身价值。德育目标Guide the students to strengthen the study of team spirit, and trulyMoral Objectivesexperience the strong team strength.Make students realize that thestrength of individuals is limited, only individuals into the collectiveteam, through efficient communication, good cooperation, canstimulate infinite power, to realize their own value.条件分布和条件期望重点：Conditional distributions and conditional expectationKey Points随机变量的函数Functions of random variables指数分布及其与泊松分布的关系；条件分布和条件期望难点：Exponential distribution and its relation to Poisson distribution; ConditionalFocal Pointsdistributions and conditional expectation知识单元序号：支撑教学目标：61-6Knowledge Unit No.SLOs Supported知识单元名称生成函数，随机变量的和Unit TitleGenerating functions, Sums of random variables生成函数知识点：Generating functionsKnowledge Delivery随机变量的和Sums of random variables生成函数掌握：学习目标：Generating functionsMasterLearning Objectives随机变量的和Sums of random variables德育目标无Moral ObjectivesNone重点：生成函数9 / 12

9 / 12 distributions and conditional expectation; Functions of random variables 知识点: Knowledge Delivery 指数分布及其与泊松分布的关系 Exponential distribution and its relation to Poisson distribution 条件分布和条件期望 Conditional distributions and conditional expectation 随机变量的函数 Functions of random variables 学习目标: Learning Objectives 了解: Recognize 指数分布及其与泊松分布的关系 Common operations about directories and files 掌握: Master 条件分布和条件期望 Conditional distributions and conditional expectation 随机变量的函数 Functions of random variables 德育目标 Moral Objectives 引导同学们加强团队精神的学习，真正体会到团队力量的强大。使 学生意识到：个人的力量是有限的，只有个人投入到集体团队中， 通过高效沟通、良好协作，才能激发出无限力量，实现自身价值。 Guide the students to strengthen the study of team spirit, and truly experience the strong team strength.Make students realize that the strength of individuals is limited, only individuals into the collective team, through efficient communication, good cooperation, can stimulate infinite power, to realize their own value. 重点: Key Points 条件分布和条件期望 Conditional distributions and conditional expectation 随机变量的函数 Functions of random variables 难点: Focal Points 指数分布及其与泊松分布的关系；条件分布和条件期望 Exponential distribution and its relation to Poisson distribution; Conditional distributions and conditional expectation 知识单元序号: Knowledge Unit No. 6 支撑教学目标: SLOs Supported 1-6 知识单元名称 Unit Title 生成函数，随机变量的和 Generating functions, Sums of random variables 知识点: Knowledge Delivery 生成函数 Generating functions 随机变量的和 Sums of random variables 学习目标: Learning Objectives 掌握: Master 生成函数 Generating functions 随机变量的和 Sums of random variables 德育目标 Moral Objectives 无 None 重点: 生成函数

Key PointsGenerating functions随机变量的和Sums of random variables难点：随机变量的和Focal PointsSums of random variables知识单元序号支撑教学目标：71-7, 2-7Knowledge Unit No.SLOs Supported知识单元名称马尔可夫链Unit TitleMarkov Chains离散马尔可夫链Discrete MarkovChains知识点：马尔可夫链分类Knowledge DeliveryClassification of MarkovChains可约性，周期性、瞬态、吸收状态Reducibility,periodicity, recurrent/transient/absorbing states了解：马尔可夫链分类RecognizeClassificationof MarkovChains离散马尔可夫链学习目标：Discrete Markov ChainsLearning Objectives掌握：可约性，周期性、瞬态和吸收状态MasterReducibility,periodicity,recurrent/transient/absorbingstates明确事物的普遍联系性和事物是不断变化发展的唯物主义观点，提高学生正确认识问题、分析问题解决问题的能力。德育目标Clarify the general connection of things and things is the changingMoral Objectivesmaterialist view, and improve students' ability to correctly understand,analyze and solveproblems.条件分布和条件期望重点：Conditional distributions and conditional expectationKey Points随机变量的函数Functions of random variables指数分布及其与泊松分布的关系；条件分布和条件期望难点：Exponential distribution and its relation to Poisson distribution; ConditionalFocal Pointsdistributions and conditional expectation四、教学安排TeachingSchedule注：可根据实际情况增减行数Note: Please add/reduce lines based on subject.学时(周)Hour(Week)教学内容 Teaching Content理论实验课外实践集中实践LECT.EXP.PBLPRAC.10/12

10 / 12 Key Points Generating functions 随机变量的和 Sums of random variables 难点: Focal Points 随机变量的和 Sums of random variables 知识单元序号: Knowledge Unit No. 7 支撑教学目标: SLOs Supported 1-7，2-7 知识单元名称 Unit Title 马尔可夫链 Markov Chains 知识点: Knowledge Delivery 离散马尔可夫链 Discrete Markov Chains 马尔可夫链分类 Classification of Markov Chains 可约性, 周期性、瞬态、吸收状态 Reducibility, periodicity, recurrent/transient/absorbing states 学习目标: Learning Objectives 了解: Recognize 马尔可夫链分类 Classification of Markov Chains 掌握: Master 离散马尔可夫链 Discrete Markov Chains 可约性, 周期性、瞬态和吸收状态 Reducibility, periodicity, recurrent/transient/absorbing states 德育目标 Moral Objectives 明确事物的普遍联系性和事物是不断变化发展的唯物主义观点，提 高学生正确认识问题、分析问题解决问题的能力。 Clarify the general connection of things and things is the changing materialist view, and improve students' ability to correctly understand, analyze and solve problems. 重点: Key Points 条件分布和条件期望 Conditional distributions and conditional expectation 随机变量的函数 Functions of random variables 难点: Focal Points 指数分布及其与泊松分布的关系；条件分布和条件期望 Exponential distribution and its relation to Poisson distribution; Conditional distributions and conditional expectation 四、教学安排 Teaching Schedule 注：可根据实际情况增减行数 Note: Please add/reduce lines based on subject. 教学内容 Teaching Content 学时(周) Hour(Week) 理论 LECT. 实验 EXP. 课外实践 PBL 集中实践 PRAC