Title:

# Statistics, Stochastic Procesess, Operational Analysis

Code:DMA1
Ac.Year:2008/2009
Term:Winter
Study plans:
ProgramBranchYearDuty
CSE-PHD-4DVI4-Elective
IT-PHD-3DIT3-Elective
Language:Czech
Completion:examination (verbal)
Type of
instruction:
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Hours:390000
ExaminationTestsExercisesLaboratoriesOther
Points:1000000
Guarantee:Baštinec Jaromír, doc. RNDr., CSc., DMAT
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT

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.
Description:
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.
Learning outcomes and competences:
The graduate of this course should be able to solve the optimising 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-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
Fundamental literature:
1. Zapletal, J.: Úvod do analýzy ekonomických časových řad. PC-DIR, VUT, Brno 2000.
2. Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995
3. Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.
4. Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
5. 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.
6. Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley & Sons, Inc., New York 2003.
7. Loftus, J., Loftus, E.: Essence of Statistics. Second Edition, A. A. Knopf, New York, 1988
8. Aramanovič, J. G., Lunc, G. L., Elsgolc, L. C., Funkcie komplexnej premennej, operátorový počet, teória stability, Alfa, SNTL, 1973.