(in Polish) Rachunek prawdopodobieństwa i wnioskowanie statystyczne WSE-EKN-RPWS
Lecture 1: Foundations of Probability in the Context of Economic Sciences
- Historical Origins and Evolution of Probabilistic Thinking in Economic Sciences
- Construction of Probability Space: Elementary Events, Event Algebra, and Its Properties
- Kolmogorov's Axiomatic Definition of Probability and Its Mathematical Consequences
- Classical, Geometric, and Frequentist Approaches to Probability in Research Practice
- Implementations in Economics and Finance: Modeling Investment Risk, Decision Uncertainty, and Stochastic Processes in the Economy
Lecture 2: Theory of Random Variables and Probability Distributions in Economic Analysis
- The Concept of Discrete and Continuous Random Variables as Mathematical Models of Economic Phenomena
- Characteristics of Distribution Functions, Densities, and Cumulative Distributions and Their Economic Interpretation
- Numerical Measures of Distributions: Expected Value, Variance, Higher-Order Moments, and Their Meaning
- Systematic Review of Key Distributions and Their Applications in Economic Modeling:
o Distributions Discrete: two-point (Bernoulli), binomial, Poisson, geometric, hypergeometric
o Continuous distributions: uniform, exponential, normal, lognormal, gamma, beta, Pareto
- Transformations and combinations of random variables in modeling complex economic phenomena
Lecture 3: Advanced theory of conditional probability and independence in economic modeling
- The concept and formalization of conditional probability in the context of economic decisions
- The extended formula for total probability and its analytical applications
- Bayes' theorem and its implementation in knowledge updating processes under uncertainty
- Independence of events and random variables - theoretical and practical implications
- Characterization of multivariate random variables: joint, marginal, and conditional distributions in the analysis of economic interdependencies
- Covariance and correlation coefficient as measures of stochastic dependence in economic modeling
- Practical applications in systemic risk quantification and modeling Decision-making processes under uncertainty
Lecture 4: Limit theorems and asymptotic properties of distributions in economic theory (3 hours)
-Theoretical foundations of sequences of random variables in modeling economic processes
• Typology of convergence of random variables and its importance in the estimation of economic parameters
• The law of large numbers in its weak and strong approaches - theoretical foundations and practical consequences
• The central limit theorem and its variants for various classes of random variables
• Implications of limit theorems for estimation methodology and hypothesis testing in econometrics
• Applications in financial risk analysis: Value at Risk, Expected Shortfall, extreme modeling
• Implications for macroeconomic modeling and economic forecasting
Lecture 5: Advanced methods of statistical inference and multivariate analysis of economic data (3 hours)
• Comprehensive estimation theory: properties of estimators and optimization criteria
• Advanced methods of estimator construction: method of moments, Maximum likelihood method, Bayesian estimators
• Interval estimation methodology: construction and interpretation of confidence intervals in the context of economic decisions
• Theory of statistical hypothesis testing: the Neyman-Pearson paradigm, type I and II errors, test power function.
(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się
(in Polish) Grupa przedmiotów ogólnouczenianych
(in Polish) Opis nakładu pracy studenta w ECTS
Subject level
Learning outcome code/codes
Type of subject
Preliminary Requirements
Course coordinators
Learning outcomes
W01: Precisely defines and comprehensively explains the fundamental concepts of probability theory: probability space, random event algebra, univariate and multivariate random variables, probability distribution and density functions, and their mathematical properties.
W02: Comprehensively characterizes the most important probability distributions used in modeling economic phenomena (binomial, Poisson, hypergeometric, normal, lognormal, Student's t-test, chi-square, Snedecor's F-test) and identifies their practical applications in economic, financial, and business analysis.
W03: Detailed explanation of the mechanisms of conditional probability, independence of events and random variables, and the implications of Bayes' theorem for knowledge updating processes under uncertainty.
W04 Thoroughly explains the Law of Large Numbers (in its weak and strong versions) and the Central Limit Theorem, along with their implications for statistical inference methodology and economic forecasting.
W05: It provides a detailed distinction and characterization of point estimation methods (method of moments, maximum likelihood method) and interval estimation methods (construction of confidence intervals), as well as statistical hypothesis testing methodology (classical and Bayesian approaches). U01: Professionally designs a methodologically sound sampling design appropriate to the specific nature of the research problem, taking into account potential limitations, systematic and random errors, and financial implications. U02: Proficiently calculates the probabilities of complex events, expected values, variances, and other characteristics of random variables in the context of practical economic, financial, and business problems. U03: Independently performs point and interval estimation of population parameters and comprehensively interprets the obtained results in the context of economic and management decisions. U04: Methodologically correctly formulates and verifies statistical hypotheses regarding distribution parameters and complex relationships between economic variables, taking into account test power and error control. U05: Efficiently performs multi-faceted statistical analyses and professional data visualizations using spreadsheets and specialized programs with a graphical interface (Excel with analytical add-ons, SPSS/PSPP). U06: Professionally prepares comprehensive analytical reports containing in-depth interpretations of statistical results and strategic business recommendations for various management levels.
K01: Effectively collaborates within an interdisciplinary team in implementing a complex analytical project, assuming various roles and responsibilities, including managerial and specialist roles.
K02: Professionally communicates the results of advanced statistical analyses in a transparent manner tailored to diverse audiences, taking into account their level of technical knowledge and information needs.
K03: Systematically and comprehensively assesses the quality of data sets, the methodological assumptions of the statistical techniques used, and the reliability and limitations of the analytical conclusions drawn.
K04: Consistently adheres to the principles of professional ethics in the process of collecting, analyzing, and presenting data, with particular emphasis on methodological transparency and interpretative objectivity.
K05: Systematically develops and updates specialist knowledge and practical skills in the dynamically evolving field of statistical methods and their implementation in economics.
K06: Fully appreciates the strategic importance of an approach based on reliable data analysis in decision-making processes at various levels of management in economic organizations, financial institutions, and public administration.
Assessment criteria
Final grade components with assigned weights:
• Oral exam * team project: 75% of the final grade
• Participatory activity + class attendance: 25% of the final grade
Substantive scope: Comprehensive lecture material with an emphasis on knowledge integration
• Grading system: Point scale with progressive percentage thresholds
o 91-100% of possible points: Very good (5.0)
o 81-90% of possible points: Good plus (4.5)
o 71-80% of possible points: Good (4.0)
o 61-70% of possible points: Satisfactory plus (3.5)
o 51-60% of possible points: Satisfactory (3.0)
o 0-50% of possible points: Failing (2.0)
Team Project Multi-stage:
•Carried out in interdisciplinary teams of 3-4 people with rotating roles and responsibilities
•Includes comprehensive analysis of an authentic, multidimensional set of economic data using advanced statistical techniques
•Systematic evaluation of components:
o Methodological correctness and adequacy of the analytical techniques used (30%)
o Depth and multi-facetedness of the analysis and innovativeness of the research approach (25%)
o Substantive quality of the interpretation of results and the strategic value of the business recommendations (25%)
o Professionalism of the analytical report and communicative effectiveness of the presentation (20%)
•Each team member receives an individualized assessment that takes into account their personal substantive and organizational contributions (based on systematic peer evaluation and observation by the instructor).
Bibliography
Required Reading:
1. Aczel A.D., Sounderpandian J., "SStatystyka w zarządzaniu: pełny wykład", PWN Scientific Publishing House (latest edition) - a comprehensive study with an emphasis on economic applications
2. Maria Balcerowicz-Szkutnik, Elżbieta Sojka, Włodzimierz Szkutnik, Statistical Inference in Examples and Problems, 2nd ed., 2016, ISBN 978-83-7875-286-8
3. Instructor's own teaching materials (sent electronically)
4. Janusz Zacharski, Probability Theory for Economists, University of Economics and Information Technology, 2001, ISBN: 83-8844-212-0
Supplementary Reading:
1. Michał Major, Elements of Statistics: Probability Theory and Statistical Inference; Krakow Educational Society - Oficyna Wydawnicza AFM, 2007, ISBN: 9788389823274
2. Górecki T., Basics of statistics with examples in R, BTC, 2011
tical in examples and tasks, WUEK, 2016 (2nd ed.), 978-83-7875-286-8
3 Efron B., Tibshirani R. J., An Introduction to the Bootstrap, Chapman & Hall/CRC Monographs on Statistics and Applied Probability, No. 57, 1993, x + 436 pp.– ISBN 0-412-04231-2 (hardcover)– ISBN 0-412-04232-0 (paperback).
Additional information
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