概率论与数理统计（英） (Probability and Statistics)
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spContent=《概率论与数理统计》是研究随机现象统计规律性的一门数学学科，是大学理工科、管理学科及大部分文科各专业的重要公共基础课程，在高等学校新工科、新文科、新医科和新农科等人才培养中占有非常重要的地位。本课程的主要内容包括概率论的基本概念、随机变量及其分布、随机变量的数字特征、大数定律、中心极限定理、抽样分布、参数估计和假设检验等。 本课程为全英文授课，主要面向来华留学本科学生和中外合作办学项目本科学生，充分迎合我国当前国际化人才培养的紧迫需求。在课程内容的设计上，强化与专业学习的相融性，注重学科交叉，提高学习兴趣。为专业课、后继课学习及毕业后的工作、深造奠定必要的数学基础，同时提升学生的统计思想、逻辑思维能力、分析判断问题能力、创新能力和应用能力。
—— 课程团队
课程概述

Probability and Statistics has become a common wisdom in a world of big data. It is a mathematical discipline which deals with random phenomena. Now it is widely used in industry, economics, science and technologies. This course is one of the important basic courses for almost all majors in universities.


This introduction course will cover the general conceptions and methods about probability and statistics. The main topics include basic probability concepts, one or more random variables and their distributions, expectations and moments of random variables, the law of large numbers and central limit theorems, sampling distributions, parameter estimation and hypothesis testing. 


Upon completion of this course, you can gain terminology, classifications and methods of probability and statistics and you will:


1) know the basic axioms and set theory upon which probability theory is based


2) solve problems by counting probabilities by means of properties and some important formulas (conditional probability, independence, and Bayes theorem)


3) understand the concept of random variables and describe their probability distributions by cdf, pmf, or pdf 


4) understand joint, marginal, and conditional distributions


5) grasp several important discrete or continuous random variables (Bernoulli distribution, binomial distribution, Poisson distribution, Hypergeometric distribution, Uniform distribution, Exponential distribution, Normal distribution and etc),  and know when to use them


6) determine the distribution of a general function of one or more random variables


7) understand and find the mean and variance of a random variable


8) understand and find covariance and correlation of two random variables


9) be able to apply the theory of expectation to solve decision problems involving the maximization of expected return


10) know and understand the law of large numbers, the central limit theorem and how to use them in practice


11) grasp some numerical and graphical methods to explore data


12) know various well-known sampling distributions and how they are used in inferential statistics


13) grasp two types of estimation techniques (method of moments and maximum likelihood estimate)


14) know several criteria for the point estimator


15) understand confidence intervals


16) construct confidence intervals for parameters of one or two normal populations


17) understand basic thoughts of hypothesis testing


18) test hypotheses about parameters concerning one or two normal populations

课程大纲
预备知识

Basic Calculus is a pre-requisite. You should take Calculus at first, or have taken it already, since we will use some material from Calculus (derivatives, integrals, partial derivatives and double integrals, some knowledge about series) later in this course.

证书要求

为积极响应国家低碳环保政策， 2021年秋季学期开始，中国大学MOOC平台将取消纸质版的认证证书，仅提供电子版的认证证书服务，证书申请方式和流程不变。

 

电子版认证证书支持查询验证，可通过扫描证书上的二维码进行有效性查询，或者访问 https://www.icourse163.org/verify，通过证书编号进行查询。学生可在“个人中心-证书-查看证书”页面自行下载、打印电子版认证证书。

 

完成课程教学内容学习和考核，成绩达到课程考核标准的学生（每门课程的考核标准不同，详见课程内的评分标准），具备申请认证证书资格，可在证书申请开放期间（以申请页面显示的时间为准），完成在线付费申请。

 

认证证书申请注意事项：

1. 根据国家相关法律法规要求，认证证书申请时要求进行实名认证，请保证所提交的实名认证信息真实完整有效。

2. 完成实名认证并支付后，系统将自动生成并发送电子版认证证书。电子版认证证书生成后不支持退费。


参考资料

1.《工科概率统计（英文版）》，魏军强，郑宏文，清华大学出版社&北京交通大学出版社，2018年版

2. 《Probability and Statistics 》(4th Edition)，Morris H. DeGroot, Mark J. Schervish，China Machine Press，2012年版

3. 《Probability and Statistics for Engineering and the Sciences 》(8th Edition)，Jay L. Devore，Cengage Learning Press，2011年版