Course detail
Statistics, Stochastic Processes, Operations Research
FEKT-DMA1Acad. year: 2011/2012
The course i s composed of three thematic units of common basis:
1) Probability and statistical processing of data, basic statistical tests and the possibilities of their use.
2) Characteristics of stochastic processes, Markov chains, staionary and ergodic processes.
3) Linear programming, transportation problem. Dynamic programming, models of stack resourses.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Basic notions from probability and statistics. Statistical sets. Point and interval estimates.Testing hypotheses with parametres (not only for normal distribution). Tests of the form of distribution. Regression analysis. Tests of good accord. Non-parametric tests.
II. Stochastic processes(4 weeks)
Deterministic and stochastic problems. Characteristics of stochastic processes. Limit, continuity, derivation and integral of a stochastic process. Markov, stationary, and ergodic processes. Canonical and spectral division of a stochastic process.
III. Operation analysis (4 weeks)
Principles of operation analysis, linear and nonlinear programming. Dynamic programming, Bellman principle of optimality. Theory of resources. Floating averages and searching hidden periods.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.
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.
Nagy, I.: Základy bayesovského odhadování a řízení, ČVUT, Praha, 2003
Škrášek, J., Tichý, Z.: Základy aplikované matematiky III. SNTL Praha, 1990
Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995
Recommended reading
Classification of course in study plans
- Programme EKT-PP Doctoral
branch PP-KAM , 1 year of study, winter semester, elective general
branch PP-SEE , 1 year of study, winter semester, elective general
branch DP-TEE , 1 year of study, winter semester, elective general
branch PP-TLI , 1 year of study, winter semester, elective general
branch PP-MET , 1 year of study, winter semester, elective general
branch PP-EST , 1 year of study, winter semester, elective general
branch PP-FEN , 1 year of study, winter semester, elective general
branch PP-MVE , 1 year of study, winter semester, elective general
branch PP-BEB , 1 year of study, winter semester, elective general - Programme EKT-PK Doctoral
branch PK-FEN , 1 year of study, winter semester, elective general
branch PK-MVE , 1 year of study, winter semester, elective general
branch PK-TEE , 1 year of study, winter semester, elective general
branch PK-TLI , 1 year of study, winter semester, elective general
branch PK-EST , 1 year of study, winter semester, elective general
branch PP-BEB , 1 year of study, winter semester, elective general
branch PK-KAM , 1 year of study, winter semester, elective general
branch PK-SEE , 1 year of study, winter semester, elective general
branch PK-MET , 1 year of study, winter semester, elective general - Programme EKT-PPA Doctoral
branch PP-FEN , 1 year of study, winter semester, elective general
branch PP-MVE , 1 year of study, winter semester, elective general
branch PP-BEB , 1 year of study, winter semester, elective general
branch PP-EST , 1 year of study, winter semester, elective general
branch PP-SEE , 1 year of study, winter semester, elective general
branch PP-TEE , 1 year of study, winter semester, elective general
branch PP-TLI , 1 year of study, winter semester, elective general
branch PP-MET , 1 year of study, winter semester, elective general
branch PP-KAM , 1 year of study, winter semester, elective general - Programme EKT-PKA Doctoral
branch PK-FEN , 1 year of study, winter semester, elective general
branch PK-MVE , 1 year of study, winter semester, elective general
branch PK-TEE , 1 year of study, winter semester, elective general
branch PK-TLI , 1 year of study, winter semester, elective general
branch PK-EST , 1 year of study, winter semester, elective general
branch PK-BEB , 1 year of study, winter semester, elective general
branch PK-KAM , 1 year of study, winter semester, elective general
branch PK-SEE , 1 year of study, winter semester, elective general
branch PK-MET , 1 year of study, winter semester, elective general
Type of course unit
Seminar
Teacher / Lecturer
Syllabus
Basic notions from probability and statistics. Statistical sets. Point and interval estimates.Testing hypotheses with parametres (not only for normal distribution). Tests of the form of distribution. Regression analysis. Tests of good accord. Non-parametric tests.
II. Stochastic processes(4 weeks)
Deterministic and stochastic problems. Characteristics of stochastic processes. Limit, continuity, derivation and integral of a stochastic process. Markov, stationary, and ergodic processes. Canonical and spectral division of a stochastic process.
III. Operation analysis (4 weeks)
Principles of operation analysis, linear and nonlinear programming. Dynamic programming, Bellman principle of optimality. Theory of resources. Floating averages and searching hidden periods.