CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

# Mathematics for Economy

Code Completion Credits Range Language
BE1M01MEK Z,ZK 6 4P+2S English
Lecturer:
Kateřina Helisová (guarantor)
Tutor:
Kateřina Helisová (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

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.

Requirements:
Syllabus of lectures:

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.

Syllabus of tutorials:

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.

Study Objective:
Study materials:

[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 &amp; Sons, 2001.

Note:
Further information:
http://math.feld.cvut.cz/helisova/01pstimfe.html
Time-table for winter semester 2021/2022:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT2:C4-78Helisová K.12:45–14:15(lecture parallel1)DejviceT2:C4-78roomT2:C4-78Helisová K.16:15–17:45(lecture parallel1parallel nr.101)DejviceT2:C4-78 roomT2:C4-78Helisová K.14:30–16:00(lecture parallel1)DejviceT2:C4-78
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-15
For updated information see http://bilakniha.cvut.cz/en/predmet4863506.html