# Subject description - BE1M01MEK

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BE1M01MEK Mathematics for Economy
Roles:  Extent of teaching:4P+2S
Department:13101 Language of teaching:EN
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:6
Tutors:  Semester:Z

Web page:

http://math.feld.cvut.cz/helisova/01pstimfe.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:

  Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.  Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.  Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern actuarial risk theory. Kluwer Academic Publishers, 2004.  Gerber, H.U.: Life Insurance Mathematics. Springer-Verlag, New York-Berlin-Heidelberg, 1990.  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 10.12.2023 05:51:51, semester: Z,L/2023-4, L/2022-3, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)