《概率论与数理统计II》课程教学大纲英文版.docx

Syllabus ofProbability Theory and Mathematical Statistics IICourse Name： Probability Theory and Mathematical Statistics II Course Code：Credits： 2Total Credit Hours： 32Lecture Hours： 32Experiment Hours： 0Programming Hours： 0Practice Hours： 0Total Number of Experimental (Programming) Projects 0 ,Where, Compulsory ( 0 ), Optional ( 0 ).School： School of ScienceTarget Major： Light Industry and Technology MajorsI、Course Nature & AimsProbability Theory and Mathematical Statistics II is a basic course for undergraduates in light industry and technology majors in our school, and this course belongs to the general course of subject platform curriculum in the mechanical and electrical professional training program, which focuses on theoretical training. The basic task of this course is to make students understand the statistical regularity of random phenomena, to understand and master the basic concepts of probability theory and mathematical statistics, to master the basic theory of statistical regularity of random phenomena and the basic methods to solve random problems, to master the basic skills of collecting, processing and analyzing random data, to cultivate students* ability to infer and predict the problems of actual random phenomena, and to lay a certain mathematical foundation for the statistical analysis and processing of random data in the subsequent professional courses of mechanical and electrical majors.II > Course Objectives1. Moral Education and Character Cultivation.This course mainly discusses the statistical law of random phenomena and the method of inferring the whole according to the local, which has wide applications and contains a wealth of political elements, such as strict thinking study habits, values of integrity and pragmatism, the dialectical relationship between the whole and the local. In the teaching process of this course, students can understand the power of mathematical thought and appreciate the beauty of mathematics through the penetration of mathematical thought; the theoretical training of probability theory can help students to cultivate students* strict, honest and pragmatic attitude of governance; it can help students to build cultural self-confidence and patriotism through integration China's scientific achievements into teaching class; it can train students' innovative thinking and critical thinking and help students to establish scientific thinking methods and the spirit of courage to face challenges in their work through the creation of problem situations. In short, through the systematic study of this course, it can help students understand the development of the subject, master the scientific world view, methodology, and promote the establishment of a correct world view and values.2. Course ObjectivesThrough the study of this course, students1 qualities, skills, knowledge and abilities obtained are as follows：Objective 1. Understand and master the basic concepts, basic nature and basic methods of solving the problem of random probability, master the classical theoretical system of probability theory, and cultivate the students* ability to analyze and solve practical problems in the comprehensive application of the basic knowledge of probability. (Corresponding to Chapter 1, supporting for graduation requirements index 2.1)Objective 2. Understand the basic concepts of random variables, probability distributions of random variables and numerical characteristics of random variables, and master the basic theory and basic computational skills of using random variables to describe probability problems and solve actual probability problems. (Corresponding to Chapter 2, 3, 4, supporting for graduation requirements index 2.1, 3.1)Objective 3. Understand the basic concepts of the law of large numbers and central limit theorem, parameter estimation, hypothesis testing, and so on, cultivate and improve students* ability to describe data, analyze data and process data, develop students' statistical thinking ability and quality, enhance students' ability to quantify research and quantitative analysis, and cultivate students' ability to make scientific inferences and solve practical engineering problems using mathematical statistical theory. (Corresponding to Chapter 5, 6, supporting for graduation requirements index 3.1)Supporting for Graduation RequirementsThe graduation requirements supported by course objectives are mainly reflected in the graduation requirements indices 2.1, 3.1, as follows:Supporting for Graduation RequirementsCourseObjectivesGraduationRequirementsIndices and Contents Supporting for GraduationRequirementsTeachingTopicsLevel ofSupportIndicesContentsObjective 12. EngineeringknowledgeIndex2.1Ability to use basic concepts, basic theories, and basic methods of mathematics, physics, and statistics for the proper expression of engineering problemsChapter 1,2,3HObjective 23. ProblemsolvingIndex3.1Be able to use relevant scientific principles to analyze and identify complex engineeringChapter 4,5,6Hproblems in the computer field, and determine its key links, steps, parameters and constraintsObjective 3Objective 4JU、Basic Course ContentChapter 1 Random events and their probabilities (supporting course objective 1)1.1 Random events1.2 Probability of random events1.3 Conditional probability1.4 Independent events and their probabilitiesTeaching Requirements: Through systematic study of random events and their probability theory, to understand the concept of sample space, to understand the probability of random events, the probability of events, the probability of conditions, the independence of events and the concept of independent repetition experiments, to be familiar with the relationship between random events and the basic nature of operations and probabilities, to master the addition formula of probability, subtraction formula, multiplication formula, full probability formula and Bayesian formula, to master the classical probability model, geometric probability model and independent repeat test probability model calculation method. Have a certain logical reasoning ability and the ability to solve practical problems by using the nature, formula and calculation method of random event probability.Key Points： The concept of probability, the basic nature and formula of probability, the calculation of the method of probabilityDifficult Points： Multiplication formula of probability, formula of total probability, Bayesian formulaChapter 2 Random variables and their probability distribution (supporting course objective 2)2.1 Distribution of random variables and their probability distribution functions2.2 Discrete random variables2.3 Continuous random variables and their probability density2.4 Distribution of random variable functionsTeaching Requirements: Through systematic study of the theory of probability distribution of one-dimensional random variables, to understand the concepts of random variables, distribution functions, discrete random variables and their distribution and continuous random variables and their probability density, familiar with the nature of distribution functions, distribution laws and probability densities, to master the 0-1 distribution, dioral distribution, geometric distribution, hypergeometric distribution, Poisson distribution, uniform distribution, exponential distribution, normal distribution and other important probability distribution models, and master the random application of variables and the study of random probability The method of distribution of random variable functions has a certain degree of probability calculation and comprehensive ability to solve practical problems.Key Points： Continuous random variables and their probability distribution, uniform distribution, exponential distribution, normal distributionDifficult Points： Distribution of exponential distribution, normal distribution, random variable functionChapter 3 Multidimensional random variables and their distribution (supporting course objective 2)3.1 Multidimensional random variables and their distribution3.2 The independence of Random variables3.3 Distribution of Multidimensional random variable functionsTeaching Requirements: Through systematic study of the theory of probability distribution of multi-dimensional random variables, we understand the concept of distribution of multi-dimensional random variables and multi-dimensional random variables, understand the probability distribution, edge distribution, condition distribution, two-dimensional continuous random variable probability density, edge density, condition density, independence and non-relevance of two-dimensional continuous random variables, familiar with the probability distribution, edge distribution and condition distribution properties of two-dimensional random variables, and understand the two-dimensional random distribution, two-dimensional distribution, two-dimensional distribution, understanding of the normal distribution of two-dimensional random variables. Mastering the application of two-dimensional random variables to discuss and calculate the probability law of random events, judging the independence of random variables and the distribution of two simple functions of random variables and the distribution of several simple functions of independent random variables, has certain probability computing power and the ability to solve practical problems in an integrated manner.Key Points： Probability distribution of two-dimensional random variables, edge distribution, distribution of simple functions of random variablesDifficult Points： Distribution of simple functions of random variablesChapter 4 Numerical characteristics of random variables (supporting course objective 2)4.1 Mathematical expectations4.2 Variance and moment4.3 Covariance and correlation coefficients4.4 Laws of large numbers and central limit theoremTeaching Requirements: Through systematic study of the numerical characteristics of random variables, to understand the concepts of mathematical expectations, variances, moments, covariance, and related coefficients, to familiarize yourself with the basic properties of mathematical expectations, variances, covariance and correlation coefficients, to master the numerical characteristics of common distributions, to master the numerical characteristics of random variables and the calculation methods of mathematical expectations of random variable functions, to understand Laws of large numbers and central limit theorem with a certain degree of probability computing power and the ability to use digital features to discuss practical problems.Key Points： Mathematical expectations, variances, covariance of random variablesDifficult Points： Covariance, law of large numbers, center limit theoremChapter 5 Statistical estimation (supporting course objective 3)5.1 Basic concepts of mathematical statistics5.2 Point estimation of parameters5.3 Interval estimation of parametersTeaching Requirements: By learning the basic theory of mathematical statistics and the method of parameter estimation, the concepts of sample mean and sample variance and sample moment of simple random sample statistics are understood. Understanding of the normal population commonly used sampling distribution and t distribution chi-square distribution and F distribution, the concept and nature of understanding point estimation of parameter estimator to estimate the unbiasedness effectiveness of estimator and the concept of the confidence interval consistency interval estimation, mastering moment estimation (first moment of second order moment) maximum likelihood estimation method of a single normal population mean and variance of interval estimation, working parameter estimation ability to infer the actual problems.Key Points： Moment estimation method, maximum likelihood estimation method, interval estimationDifficult Points： Sampling distributions, maximum likelihood estimation methodChapter 6 Hypothesis testing (supporting course objective 3)6.1 Parametric hypothesis testing overview6.2 Parametric hypothesis testing of normal populationTeaching Requirements: Understand the basic idea of significance test, master the basic steps of hypothesis testing, understand the two types of errors that may be generated by hypothesis testing, master the hypothesis testing of mean and variance of a single normal populations skillfully, and have the ability to make scientific inferences and form accurate conclusions based on sample data.Key Points： The basic steps of hypothesis testing, statistical inferenceDifficult Points： The basic idea of significance testingIV、Table of Credit Hour DistributionTeaching ContentIdeological and PoliticalIntegratedLecture HoursExperiment HoursPractice HoursProgramming HoursSelf-study HoursExercise ClassDiscussion HoursChapter 1 Random events and theirprobabilitiesMathematical thoughtpenetration51Chapter 2 Random variables and theirprobability distributionRigorous scholarship51Chapter 3 Multidimensional randomvariables and their distributionInnovative thinking guidance41Chapter 4 Numerical characteristics ofrandom variablesThe power of data51Chapter 5 Statistical estimationDialectic relation of the localand the whole51Chapter 6 Hypothesis testingContradiction and unity21Total266Sum32V、Summary of Experimental (Programming) ProjectsNo experiment (programming) sessionVI、Teaching MethodThis course is dominated by teachers* classroom teaching, supplemented by self-study and after-school assignments based on the video materials of the course. The teaching process should be flexible in the use of board books and multimedia teaching, strengthen teacher-student interaction, pay attention to heuristic teaching, adopt questions for important knowledge points, analyze problems, and solve problems to teach ideas.VD、Course Assessment and Achievement EvaluationAssessment Methods： ExaminationExamination Formats： Closed-bookGrading Methods： Hundred-mark SystemCourse Assessment Content, Assessment Format and Supporting Course ObjectivesCourseObjectives (Indices)Assessment ContentAssessment Formats and Proportion ( % )GradingClassroom QuestioningAssignment EvaluationRoutine TestExperiment ReportTerm ReportTerm PaperMidterm ExamFinal ExamProportion(%)Objective1 (Index 2.1)Relations and operations of random events; Concepts and properties of probability; The concept and properties of conditional probability; Classical probability model; Geometric probability model; Independent experiment probability model55