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

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jaromír Baštinec, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

Ability to solve optimization and statistical problems from technological practice. Solving problems with the use of modern mathematical software.

Prerequisites

The knowledge of the Bachelor´s and Master's degree level courses is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Course curriculum

I. Statistics (5 weeks)
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

Not applicable.

Aims

The objecive of the course is to expand knowledge in the area of statistical tests and data sample processing, mastering the basics of operations research including the appplications in electrical engineering with the use of mathematical software.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year. The student will be able to sit the exam only after a successful solution of a project has been presented.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Papoulis, A.: Probability, Random Variables and Stochastic Processes, McGraw-Hill, 1991.
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

Type of course unit

Seminar

39 hod., optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Syllabus

VUT

Faculties

University Institutes

Parts

Statistics, Stochastic Processes, Operations Research

Type of course unit