Bachelor
2024/2025
Probability Theory and Statistics
Type:
Compulsory course (International Programme in Economics and Finance)
Area of studies:
Economics
Delivered by:
International College of Economics and Finance
When:
1 year, 1, 2 semester
Mode of studies:
offline
Open to:
students of one campus
Language:
English
ECTS credits:
8
Course Syllabus
Abstract
Introductory Probability Theory and Statistics is a two-semester course for first-year students of the ICEF. The course is taught in English. The main objective of the course is to provide students with knowledge of basic probability theory and statistics. By the end of the course the students should master mathematical foundations of probability theory and basic methods of statistical analysis of data. They should understand the notion of randomness and methods how to describe it using probability distributions, understand the concept of a random variable, know how to perform operations with random variables and to compute their basic characteristics (expectation, variance, covariance, etc.), understand main limit theorems. Furthermore, the students should know how to formulate and solve typical problems of basic statistics: descriptive analysis of data, point and interval parameter estimation, hypothesis testing.
Learning Objectives
- Give the students basic knowledge and skills of statistical analysis and its application
- Outline essential concepts of probability theory and statistics.
- Teach students how to build a statistical model of real natural or socio-economic phenomena, perform basic steps of statistical analysis, and make conclusions justified by available evidence from data
- Teach students how to use real data sets with modern econometric software
Expected Learning Outcomes
- Be able to apply basic probabilistic formulas: the formula of total probability, Bayes’ formula.
- Be able to apply the basic statistical tests for population mean and proportion variance in the cases of a one-sample study and a two-sample study.
- Be able to apply the Law of Large Numbers and the Central Limit Theorem.
- Be able to compute basic point estimates of population mean and population variance
- Be able to compute the basic characteristic of random variables: expectation, variance, covariance
- Be able to construct confidence intervals for population mean, population proportion, or population variance in the case of a one-sample selection
- Be able to construct confidence intervals for population mean, population proportion, or population variance in the case of a two-sample selection from independent populations
- Be able to formalize a sampling procedure in terms of concepts of probability theory
- Compute probabilities for continuous random variables, their expectations, variance, covariance
- Distinguish between a population and a sample
- Explain basic concepts of probability theory: random outcomes, random events, conditional probability, and independent random events
- Explain the concept of a continuous probability distribution, and a probability density function.
- Explain the concept of a random variable and its distribution
- Explain the concepts of a null hypothesis and an alternative hypothesis, type 1 and type 2 errors
- Explain the concepts of statistical bias, unbiased estimators and efficient estimators
- Be able to find conditional distribution of random variable, compute conditional expectation given random event.
- Be able to find regression line, compute slope and intercept.
Course Contents
- Elements of Probability Theory
- Discrete random variables
- Continuous random variables
- Limit theorems
- Populations and samples. Planning and organizing a statistical study
- Descriptive statistics
- Point estimation of parameters
- Confidence intervals
- Testing of statistical hypotheses
- Simple linear regression
- Bayesian statistics
- Revision
Interim Assessment
- 2024/2025 2nd semester0.09 * Activity + 0.1 * Fall midterm + 0.45 * Final exam + 0.11 * Home assignments + 0.13 * Spring midterm + 0.12 * Winter midterm
Bibliography
Recommended Core Bibliography
- All of statistics : a concise course in statistical inference, Wasserman, L., 2004
- Elementary probability for applications, Durrett, R., 2009
- Introductory statistics for business and economics, Wonnacott, T. H., 1990
Recommended Additional Bibliography
- Beck, V. L. (2017). Linear Regression : Models, Analysis, and Applications. Hauppauge, New York: Nova Science Publishers, Inc. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1562876
- Introduction to mathematical statistics and its applications, Larsen, R. J., 2014
- Statistics for business and economics, Newbold, P., 2013