Probability Theory and Mathematical Statistics

2020/2021

Учебный год

ENG

Обучение ведется на английском языке

5

Кредиты

Кто читает:

Образовательная программа «Управление цифровым продуктом»

Статус:

Курс обязательный

Когда читается:

2-й курс, 1, 2 модуль

Преподаватели

Афанасьев Антон Андреевич

Вецлер Денис Иванович

Course Syllabus

Abstract

Probability Theory and Mathematical Statistics (PT&Stat below) is a core mathematical subject taught to the second year students in the 1st and 2nd academic modules. The material is split between probability theory and statistics almost evenly. The course covers classical probability topics from basic probability to limit theorems. More attention is paid to the conditional moments of multivariate random variables. Depending on the available time more advanced topics such as random walks, the Poisson process and Markov chains may be considered. The statistical section starts with the descriptive techniques but quickly switches to the inferential methods as they are more mathematically involved and require more eorts to explain. The topics covered here include sampling distributions, point and interval estimates, hypothesis testing. We conclude with a univariate and, if time permits, multivariate regression. Throughout the course a certain balance between mathematical rigor and clarity is maintained. Sometimes this dilemma is resolved in favor of illustrative examples which help students capture the main ideas and use them in practice rather than focus on blind memorizing the derivations. However, we nd it instructive to provide the tractable proofs whenever it makes pedagogical or some other sense. The course is taught in English and worth 5 credits.

Learning Objectives

• knows some of the basic ideas of theoretical statistics, emphasising the applications of these methods and the interpretation of tables and results.
• is familiar with concepts and methods that provide the foundation for more specialised courses in statistics

Expected Learning Outcomes

• have a grounding in probability theory and some grasp of the most common statistical methods;
• be able to summarise the ideas of randomness and variability, and the way in which these link to probability theory to allow the systematic and logical collection of statistical techniques of great practical importance in many applied areas;
• recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions
• apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments;
• demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems
• be able to summarise the ideas of randomness and variability, and the way in which these link to probability theory to allow the systematic and logical collection of statistical techniques of great practical importance in many applied areas
• be able to routinely apply a variety of methods for explaining, summarising and presenting data and interpreting results clearly using appropriate diagrams, titles and labels when required
• be able to perform inference to test the significance of common measures such as means and proportions and conduct chi-squared tests of contingency tables
• explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform hypothesis tests in a number of different settings
• explain the principles of data reduction
• choose appropriate methods of inference to tackle real problems

Course Contents

• Axioms of probability
• Discrete random variables
• Jointly distributed random variable
• Conditional probability and independence
• Continuous random variables
• Limit theorems
• Methods of descriptive statistics
• Ideas of sampling and sampling distributions
• Point and interval estimates
• Hypothesis testing
• Linear regression models

Assessment Elements

• Exam
  Examination format: The exam is taken with asynchronous proctoring Asynchronous proctoring means that all the student's actions during the exam will be “watched” by the computer. The exam process is recorded and analyzed by artificial intelligence and a human (proctor). Please be careful and follow the instructions clearly! The platform: The exam is conducted on the StartExam platform. StartExam is an online platform for conducting test tasks of various levels of complexity. The link to pass the exam task will be available to the student in the RUZ. The computers must meet the following technical requirements 1. Desktop computer or laptop only (mobile devices are not supported); 2. Operating systems: Windows( v. 7, 8, 8.1, 10), Mac OS X Yosemite 10.10 and higher; 3. Google Chrome of the latest (by the day of the control) update (to download use the link: https://www.google.com/chrome/, to update follow chrome://help/ with browser version and the update button if available) or Yandex Browser of the latest update. 4. Network port data allowed: 80 TCP, 443 TCP, 3478 TCP/UDP (check it with your provider / select control panel – system and security – Miscrosoft Deneder Firewall – additional options. Make sure that your inbound and outbound connection is not limited). 5. Adjusted and turned on web-camera (including a laptop integrated one) 6. Adjusted and turned on microphone (including a laptop integrated one); 7. High-speed stable Internet access 5 Mbit/s and higher; it is not recommended to use mobile Internet access since technical failure and cutting off are highly likely to occur during proctoring control. 8. Your desktop computer or laptop must successfully complete verification which is available only after authorization. All students are expected to do their best to ensure their computers (laptops) meet all the requirements described above. A student is supposed to follow the requirements below (With proctoring): Prepare identification documents (а passport on a page with name and photo) for identification before the beginning of the examination task; Check your microphone, speakers or headphones, webcam, Internet connection (we recommend connecting your computer to the network with a cable, if possible); Prepare the necessary writing equipment, such as pens, pencils, pieces of paper, and others. Disable applications on the computer's task other than the browser that will be used to log in to the StartExam program. If one of the necessary requirements for participation in the exam cannot be met, a student is obliged to inform a program manager 7 days before the exam date to decide on the student's participation in the exams. Important rules: All rules are available in exam regulations using asynchronous proctoring technology in the framework of intermediate certification. Connection failures: A short-term connection failure during the exam is considered to be the loss of a student's network connection with the StartExam platform for no longer than 5 minutes per exam. A long-term connection failure during the exam is considered to be the loss of a student's network connection with the StartExam platform for longer than 5 minutes per exam and will be the basis for the decision to terminate the exam. In case of long-term connection failure in the StartExam platform during the examination task, the student must record the fact of connection failure (screenshot, a response from the Internet provider). Then contact the program manager with an explanatory note about the incident to decide on retaking the exam.
• MidTerm
• Homeworks
• Quizzes

Interim Assessment

• Interim assessment (2 module)
  0.45 * Exam + 0.2 * Homeworks + 0.3 * MidTerm + 0.05 * Quizzes

Bibliography

Recommended Core Bibliography

• Probability and random processes, Grimmett, G. R., 2004
• Probability and random processes, Grimmett, G. R., 2009
• Statistical inference, Casella, G., 2002
• Statistical inference, Casella, G., 2002
• Statistics for business and economics, Newbold, P., 2013
• Statistics, Freedman, D., 1998

Recommended Additional Bibliography

• Grimmett, G., & Welsh, D. J. A. (2014). Probability : An Introduction (Vol. 2nd ed). Oxford: OUP Oxford. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=852090