457-0909/01 – Mathematical Statistics and Random Process (MSNP)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. Ing. Radim Briš, CSc.Subject version guarantorprof. Ing. Radim Briš, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1992/1993Year of cancellation2010/2011
Intended for the facultiesIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
BRI10 prof. Ing. Radim Briš, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

The objective of the course is to develop sufficient knowledge of statistical tools and procedures in applied engineering fields.

Teaching methods

Individual consultations
Project work

Summary

The course will emphasize methods of applied statistics and data analysis. Theoretical considerations will be included to the extent that knowledge of theory is necessary for a sound understanding of methods and contributes to the development of data analysis skills and the ability to interpret results of statistical analysis. The objective of the course is to develop sufficient knowledge of statistical tools and procedures, understanding of the underlying theory on which the procedures are based, and facility in the application of statistical tools to enable the student to incorporate sound statistical methodology into other areas of his or her own work.

Compulsory literature:

Anděl, J.: Statistická analýza časových řad, SNTL,Praha 1975. Likeš, J., Machek, J.: Matematická statistika, MVŠT, SNTL, 1988. Kendall,M., Stuart,A.: The Advances Theory of Statistics, London, překl.Moskva, 1976. N.R.Draper, H.Smith: Applied Regression analysis, New York,1981, překl. Moskva, 1987. B.Vidacovic: Statiscal Modeling by Wavelets,1999, ISBN-0-471-29365.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Náhodné jevy a veličiny, statistické soubory. Náhodné veličiny. Rozdělení spojité, diskrétní. Charakteristická funkce. Statistické soubory, jejich charakteristiky, bodové a intervalové odhady. Kritérium maximální věrohodnosti. Bayesův přístup. Testování statistických hypotéz. Parametrické a neparametrické testy. Některé konkrétní testy normálního rozdělení. Použití statistického software Statgraphics, S-PLUS. Základy kovarianční a korelační analýzy, regresní analýza. Kovarianční a korelační matice. Koeficienty korelace a determinace. Interval spolehlivosti. Lineární regrese. Odhad parametrů a vyhodnocení regresního lineárního modelu. Nelineární regrese. ANOVA. Použití statistického software. Náhodné procesy. Náhodné funkce. Rozklad v ortogonální bázi. Autokorelační funkce stacionárních, ergodických procesů. Test a analýza autokorelace. Funkce vzájemné korelace. Časové řady. Filtrace a predikce. Spektrální analýza v ortogonální bázi. Spektrální analýza ergodického procesu. Energetické spektrum, vzájemné energetické spektrum, kospektrum, koherentní funkce. Rozklad pomocí ortogonálních waveletů. Waveletovské spektrum. Filtrace, predikce. Wavelet-Toolbox. Úvod do Markovských procesů, klasifikace Markovských řetězců.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
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2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan

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