Course details

Statistic methods of data processing

QM7 Acad. year 2005/2006 Winter semester

Current academic year

Importance of statistical methods. Describing statistics. Analysis of time series. Indexes analysis. Random events and probability. Random variable and its characteristics. Random vector. The important distributions. Mathematical statistics. The testing of hypotheses. Regression analysis.

Guarantor

Zapletal Josef, doc. RNDr., CSc.

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

The graduate of course would be able to use possibilities of statistical analysis for solving of concreete research problems of technical practice.

Learning objectives

To show the possibilites of statistical methods for solving of research problems in technical research on concrete examples.

Prerequisite knowledge and skills

Rudiments of statistics methods.

Study literature

  • Anděl J.Matematická statistika. SNTL/Alfa, Praha1978.
  • Hátle J. Likeš J. Základy počtu pravděpodobnosti a matematické statistiky.SNTL/Alfa, Praha 1974.
  • Likeš J. Machek J. Matematická statistika ,SNTL, Praha, 1983.
  • Likeš J. Machek J. Počet pravděpodobnosti,SNTL, Praha, 1981.
  • Zapletal J. Základy počtu pravděpodobnosti a matematické statistiky. PC-DIR, VUT, Brno 1995.

Fundamental literature

  • Anděl J. Statistické metody. Matfyzpress, KU Praha 1993
  • Cochran W.G. Sampling techniques. Wiley, New York 1953.
  • Hájek J., Šidák Z. Theory of rank tests., Academia, Praha, 1967.
  • Kendall M.G., Stuart A. The advanced theory of statistics.Griffin, London 1969.
  • Likeš J. Machek J. Matematická statistika ,SNTL, Praha, 1983.
  • Šor J.B. Statistické metody analýzy a kontroly jakosti a spolehlivosti. SNTL,Praha, 1965.
  • Zvára K.Regresní analýza. Academia, Praha 1989.

Syllabus of lectures

  • Describing statistics. The basic sample. Statistical signs. One-dimensional statistical samples with quantitatv sign. Frequency.
  • Time series analysis. Trends. Floating means. Periodicity. Correlations.
  • Indexes analysis. Individual indexes. Summary indexes. Indexes and absolute values. Basical and string indexes.
  • Elementarz random event, operations among events. Boolean algebra of events. Classical and axiomatical definition of probability. The notion of independence of events. Bernoully sequences.
  • The random variable, the distributive function. Random vector.Simultaneous and marginal function of density and distributive function.
  • Moment's characteristics.General moments and central moments.
  • Some important distrubutions applicable on solving of problems of opereach research and important for statistical research.
  • The law of great numbers. Limit theorems.
  • The notion of random sample. The sample characteristics - statistics. Testing of hypotheses. Errors of the first and second kind. Parametrical tests.
  • Testing of one group of samples.
  • Application of the department§s software on various groups tests - without interaction, with interaction.
  • Chi square test, Kolmogorov-Smirnov test.
  • Correlation analysis. Sperman's correlation coefficient.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

The form of consultations.

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