CTU FEE Moodle
Mathematics for Economy
B252 - Summer 25/26
This course is not present in Moodle. You can visit its homepage by clicking the "Course page (outside Moodle)" button on the right (if available).
Mathematics for Economy - B1B01MEK
| Credits | 5 |
| Semesters | Summer |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 3P+2S |
Annotation
The aim is to introduce the basic theory of probability and statistics, familiarise students with basic terms properties and methods used in working with random processes, especially with Markov chains, and show applications of these mathematical tools in economics and insurance.
Study targets
None
Course outlines
1. Basics of probability - random event, conditional probability, Bayes theorem
2. Random variable - definition, distribution function, basic characteristics of random variables - mean value, variance.
3. Importance of some discrete random variables in economics, Poisson and binomial distribution.
4. Importance of some continuous random variables in economics, exponential and normal distribution.
5. Random vector - definition, description, marginal distribution, covariance and correlation, independence of random variables.
6. Central limit theorem - use for basic calculations, its importance in statistics and economics.
7. Basic concepts in statistics - random sample, sample mean, sample variance, quantile, empirical distribution function, histogram, boxplot.
8. Application of probability in statistics - point and interval estimates, hypothesis testing.
9. Random processes - basic concepts.
10. Markov chains with discrete time - properties, transition probability matrix, classification of states.
11. Markov chains with continuous time - properties, transition probability matrix, classification of states.
12. Practical use of random processes - Wiener process, Poisson process, applications.
13. Regression analysis.
14. Reserve formation - basic probability distribution of the number and amount of claims, triangular schemes, Markov chains in bonus systems.
2. Random variable - definition, distribution function, basic characteristics of random variables - mean value, variance.
3. Importance of some discrete random variables in economics, Poisson and binomial distribution.
4. Importance of some continuous random variables in economics, exponential and normal distribution.
5. Random vector - definition, description, marginal distribution, covariance and correlation, independence of random variables.
6. Central limit theorem - use for basic calculations, its importance in statistics and economics.
7. Basic concepts in statistics - random sample, sample mean, sample variance, quantile, empirical distribution function, histogram, boxplot.
8. Application of probability in statistics - point and interval estimates, hypothesis testing.
9. Random processes - basic concepts.
10. Markov chains with discrete time - properties, transition probability matrix, classification of states.
11. Markov chains with continuous time - properties, transition probability matrix, classification of states.
12. Practical use of random processes - Wiener process, Poisson process, applications.
13. Regression analysis.
14. Reserve formation - basic probability distribution of the number and amount of claims, triangular schemes, Markov chains in bonus systems.
Exercises outlines
None
Literature
[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.
[2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.
[3] Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern actuarial risk theory. Kluwer Academic Publishers, 2004.
[4] Study materials (extended lecture text, presentations, practice examples) available on the course website, which is linked in Moodle.
[2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.
[3] Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern actuarial risk theory. Kluwer Academic Publishers, 2004.
[4] Study materials (extended lecture text, presentations, practice examples) available on the course website, which is linked in Moodle.
Requirements
None