Subject description - B1M01MEK

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B1M01MEK Mathematics for Economy
Roles:  Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:6
Tutors:  Semester:Z

Web page:

https://math.fel.cvut.cz/en/people/heliskat/01mekA1M01MPE.html

Anotation:

The aim is to introduce basics of probability, statistics and random processes, especially with Markov chains, and show applications of these mathematical tools in economics.

Course outlines:

1. Random events, probability, probability space, conditional probability, Bayes theorem, independent events.
2. Random variable - construction and usage of distribution function, probability function and density, characteristics of random variables - expected value, variance.
3. Discrete random variable - examples and usage.
4. Continuous random variable - examples and usage.
5. Independence of random variables, covariance, correlation, transformation of random variables, sum of independent random variables (convolution).
6. Random vector, joint and marginal distribution, central limit theorem.
7. Random sampling and basic statistics, point estimates, maximum likelihood method and method of moments.
8. Confidence intervals.
9. Hypotheses testing.
10. Random processes - basic terms.
11. Markov chains with discrete time - properties, transition probability matrix, classification of states.
12. Markov chains with continuous time - properties, transition probability matrix, classification of states.
13. Practical use of random processes - Wiener process, Poisson process, applications.
14. Linear regression.

Exercises outline:

1. Random events, probability, probability space, conditional probability, Bayes theorem, independent events.
2. Random variable - construction and usage of distribution function, probability function and density, characteristics of random variables - expected value, variance.
3. Discrete random variable - examples and usage.
4. Continuous random variable - examples and usage.
5. Independence of random variables, covariance, correlation, transformation of random variables, sum of independent random variables (convolution).
6. Random vector, joint and marginal distribution, central limit theorem.
7. Random sampling and basic statistics, point estimates, maximum likelihood method and method of moments.
8. Confidence intervals.
9. Hypotheses testing.
10. Random processes - basic terms.
11. Markov chains with discrete time - properties, transition probability matrix, classification of states.
12. Markov chains with continuous time - properties, transition probability matrix, classification of states.
13. Practical use of random processes - Wiener process, Poisson process, applications.
14. Linear regression.

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] Gerber, H.U.: Life Insurance Mathematics. Springer-Verlag, New York-Berlin-Heidelberg, 1990.
[5] Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, 2001.

Requirements:

Subject is included into these academic programs:

Program Branch Role Recommended semester

Page updated 14.3.2025 12:51:33, semester: L/2024-5, L/2025-6, Z/2024-5, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: prof. Ing. Jiří Jakovenko, Ph.D.