Mathematics for Economy
Code  Completion  Credits  Range  Language 

BE1M01MEK  Z,ZK  6  4P+2S  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 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, PrenticeHall, 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. SpringerVerlag, New YorkBerlinHeidelberg, 1990.
[5] Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. John Wiley & Sons, 2001.
 Note:
 Further information:
 http://math.feld.cvut.cz/helisova/01pstimfe.html
 No timetable has been prepared for this course
 The course is a part of the following study plans: