Course details

Statistics, Stochastic Procesess, Operational Analysis

DMA1 Acad. year 2007/2008 Winter semester

Current academic year

Basic statistical tests, i.e. t-test, F-test, chi-kvadrat test. Regression analyssis. Goodnessw of fit test. Nonparametric tests. Mathematical methods in economics - linear programming, the transport problem. Dynamic programming, inventory models. Markov chain and time series.

Guarantor

Baštinec Jaromír, doc. RNDr., CSc. (UMAT)

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

The graduate of this course should be able to solve the optimising and statistical problems of technical and economical practice.

Learning objectives

The objecive of the course is to expand knowledge in the area of statistical tests and data sample processing, Markow chain and time series, including applications in economy.

Prerequisite knowledge and skills

There are no prerequisites

Fundamental literature

  • Zapletal, J.: Úvod do analýzy ekonomických časových řad. PC-DIR, VUT, Brno 2000.
  • Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995
  • Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.
  • Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
  • Miller, I., Miller, M.: John E. Freund's Mathematical Statistics. Sixth Edition. Prentice Hall, Inc., New Jersey 1999. Předchozí vydání publikováno pod názvem Freund, J.E.: Mathematical Statistics, Fifth Edition.
  • Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley & Sons, Inc., New York 2003.
  • Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, A. A. Knopf, New York, 1988
  • Aramanovič, J. G., Lunc, G. L., Elsgolc, L. C., Funkcie komplexnej premennej, operátorový počet, teória stability, Alfa, SNTL, 1973.

Syllabus of lectures

  1. Basic concepts of probability theory
  2. Statistical samples
  3. Point and interval estimates
  4. Testing hypotheses of given parameters (not only normal distribution)
  5. Distribution tests (chi-quadrat test, Kolmogorov-Smirnov test, etc.)
  6. Operational analysis methods, linear and non-linear programming
  7. Dynamical programming, Bellman principle
  8. Markov chain, M/M/s systems
  9. Inventory models, especially random issues
  10. Replicate theory, deterministic and especcially stochastic problems.
  11. Time series
  12. Note on floating averages and hidden periods

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

There are no checked study.

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