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Course Syllabus

Бакалавриат 2021/2022

Теория вероятностей и математическая статистика

Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус: Курс обязательный
Направление: 01.03.02. Прикладная математика и информатика
Кто читает: Департамент больших данных и информационного поиска
Где читается: Факультет компьютерных наук
Когда читается: 2-й курс, 1-4 модуль
Формат изучения: с онлайн-курсом
Охват аудитории: для своего кампуса
Преподаватели: Афанасьев Антон Андреевич, Горяинов Александр Владимирович, Лукьянченко Петр Павлович
Язык: английский
Кредиты: 8
Контактные часы: 170

Course Syllabus

Full Syllabus

Abstract

This course is designed to introduce students to the basic ideas and methods of statistics as well as the application of statistical methods in econometrics, data science and the social sciences. This course provides some of the analytical tools that are required by advanced courses of data science and machine learning. This course provides students with experience in the methods and applications of statistics to a wide range of theoretical and practical situations. The course is taught in English. Prerequisites are Calculus (functions of several variables, partial derivatives, integrals, maximum of functions), and elements of Linear algebra (vectors, matrices, linear equations).
Learning Objectives

Learning Objectives

  • This course introduces some of the basic ideas of theoretical statistics, emphasizing the applications of these methods and the interpretation of tables and results.
  • We will introduce concepts and methods that provide the foundation for more specialised courses in statistics.
Expected Learning Outcomes

Expected Learning Outcomes

  • Students will be able to apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments.
  • Students will be able to choose appropriate methods of inference to tackle real problems.
  • Students will be able to 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.
  • Students will be able to explain the principles of data reduction.
  • Students will 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.
  • Students will be able to recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions.
  • Students will 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.
  • Students will 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.
  • Students will be able to use simple linear regression and correlation analysis and know when it is appropriate to do so.
  • Students will demonstrate an understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.
  • Students will have a grounding in probability theory and some grasp of the most common statistical methods.
Course Contents

Course Contents

  • Data presentation.
  • Elements of probability theory.
  • Discrete random variables.
  • Continuous random variables.
  • Multivariate random variables.
  • Conditional distributions.
  • Limit theorems.
  • The normal distribution and ideas of sampling.
  • Populations and samples.
  • Point estimation of parameters.
  • Confidence intervals.
  • Testing of statistical hypotheses.
  • Linear regression.
  • ANOVA.
  • Experiment design.
Assessment Elements

Assessment Elements

  • non-blocking fall Home assignments
  • non-blocking spring Home assignments
  • non-blocking FallMock (October Midterm)
    At the end of each module the students sit a written exam.
  • non-blocking SpringMock (Spring Midterm)
    At the end of each module the students sit a written exam.
  • non-blocking WinterExam (December Exam)
    The exam may be carried out online via distance learning platforms. At the end of each module the students sit a written exam.
  • non-blocking University of London exams (May Exam)
  • non-blocking FinalExam (June Exam)
    The exam may be carried out online via distance learning platforms. At the end of each module, the students sit a written exam. Written Exam with no proctoring. students must complete a home project. If a student is absent due to a valid excuse the exam's weight is distributed to the Winter Exam. Students who miss the deadline with no valid reason receive a 0.
Interim Assessment

Interim Assessment

  • 2021/2022 1st module
    0.7 * FallMock (October Midterm) + 0.3 * fall Home assignments
  • 2021/2022 4th module
    0.4 * FinalExam (June Exam) + 0.15 * SpringMock (Spring Midterm) + 0.4 * University of London exams (May Exam) + 0.05 * spring Home assignments
Bibliography

Bibliography

Recommended Core Bibliography

  • Statistics for business and economics, Newbold, P., 2007

Recommended Additional Bibliography

  • Bartoszyński, R., & Niewiadomska-Bugaj, M. (2008). Probability and Statistical Inference (Vol. 2nd ed). Hoboken, N.J.: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=219782
  • Freund, J. E., Miller, I., & Miller, M. (2014). John E. Freund’s Mathematical Statistics with Applications: Pearson New International Edition (Vol. Eighth edition, Pearson new international edition). Essex, England: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418305
  • Hogg, R. V., McKean, J. W., & Craig, A. T. (2014). Introduction to Mathematical Statistics: Pearson New International Edition. Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418145
  • Hogg, R. V., Zimmerman, D. L., & Tanis, E. A. (2015). Probability and Statistical Inference, Global Edition (Vol. Ninth edition. Global edition). Boston: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419274
  • Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756
  • Lindgren, B. W. (1993). Statistical Theory (Vol. Fourth edition). Boca Raton, Florida: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1683924