2024/2025
Теория вероятностей
Статус:
Маго-лего
Когда читается:
2 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
3
Course Syllabus
Abstract
The objective of the discipline "Probability Theory" is to lay the foundation of probability concepts and methodology for all courses that follow in the Data Analytics and Social Statistics programme. The course is strongly related and complementary to other compulsory courses provided in the first year (e.g. Introduction to Statistics, Applied Linear Models, Contemporary Data Analysis) and sets a crucial prerequisite for later courses and research projects as well as for the master thesis.
Learning Objectives
- The course gives students an important foundation to develop and conduct their own research as well as to evalu- ate research of others.
Expected Learning Outcomes
- Be able to define and apply the concepts of sample space, events, probability, random variables, and their distributions.
- Be able to formulate and apply the definitions of convergence in distribution and in probability, formulate scientific problems involving randomness in mathematical terms.
- Be able to formulate and apply theorems concerning functions of random variables and the moment- generating functions, Chebyshev’s theorem, the Central Limit Theorem and the Law of Large Numbers.
- Be able to use probability in future courses and analytical career overall.
- Have an understanding of the basic principles of probability and lay the foundation for future learning in the area.
- Have the skill to meaningfully develop an appropriate model for the research question, using probability theory.
- Have the skill to work with statistical software, required to analyze the data.
- Know joint probability distributions, expectation, variance and covariance of random variables.
- Know the basic principles of using probability for using analytic models.
- Know the role of probability theory in the sciences, communicate the ideas and results of probability.
Course Contents
- Axioms of probability
- Conditional probability and independence
- Discrete Random Variables
- Continuous Random Variables
- Jointly Distributed Random Variables
- Properties of Expectation
- Limit Theorems
- Additional topics in probability
Interim Assessment
- 2024/2025 2nd module0.5 * Final exam + 0.25 * Homework Assignment 1 + 0.25 * Homework Assignment 2
Bibliography
Recommended Core Bibliography
- Rohatgi, V. K., & Saleh, A. K. M. E. (2015). An Introduction to Probability and Statistics (Vol. 3rd edition). Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1050364
- Venkatesh, S. S. (2013). The Theory of Probability : Explorations and Applications. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=498312
Recommended Additional Bibliography
- Courgeau, D. (2012). Probability and Social Science : Methodological Relationships Between the Two Approaches. Dordrecht: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=523080