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# Course detail

## Statistics, Stochastic Processes, Operations Research

Subjet code : FEKT-DMA1 Faculty of Electrical Engineering and Communication 2011/2012 Yes doc. RNDr. Jaromír Baštinec, CSc. Department of Mathematics Doctoral full-time study Czech 4 examination 1 winter general knowledge

The study programmes with the given course

 Objective of the course – aims of the course unit: 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. Objective of the course – learning outcomes and competences: 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. Course contents (annotation): 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. Teaching methods and criteria: 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. 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 reading: Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley \& Sons, Inc., New York 2003. 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. Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989. Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995 Papoulis, A.: Probability, Random Variables and Stochastic Processes, McGraw-Hill, 1991. Nagy, I.: Základy bayesovského odhadování a řízení, ČVUT, Praha, 2003Škrášek, J., Tichý, Z.: Základy aplikované matematiky III. SNTL Praha, 1990

Type of course unit:
 39 hours, optionally doc. RNDr. Jaromír Baštinec, CSc.