Statistics, Stochastic Procesess, Operational Analysis

Completion:examination (verbal)
Type of
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Guarantee:Baštinec Jaromír, doc. RNDr., CSc., DMAT
Lecturer:Baštinec Jaromír, doc. RNDr., CSc., DMAT
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
Learning objectives:
  The objective of the course is to expand knowledge in the area of statistical tests and data sample processing, Markov chain and time series, including applications in economy.
  Basic statistical tests, i.e. t-test, F-test, chi-quadrant test. Regression analysis. Goodness of fit test. Nonparametric tests. Mathematical methods in economics - linear programming, the transport problem. Dynamic programming, inventory models. Markov chain and time series.
Learning outcomes and competences:
  The graduate of this course should be able to solve the optimizing and statistical problems of technical and economical practice.
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-quadrant 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 especially stochastic problems.
  11. Time series
  12. Note on floating averages and hidden periods
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.