639-2002/05 – Mathematical Statistics (MS)

Gurantor departmentDepartment of Quality ManagementCredits7
Subject guarantorprof. RNDr. Josef Tošenovský, CSc.Subject version guarantorIng. Filip Tošenovský, Ph.D.
Study levelundergraduate or graduate
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAL37 Ing. Mgr. Petra Halfarová, Ph.D.
TOS012 Ing. Filip Tošenovský, Ph.D.
TOS40 prof. RNDr. Josef Tošenovský, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Part-time Credit and Examination 24+0

Subject aims expressed by acquired skills and competences

Knowlege of Basic statistical Methods Analysis of Experimental Data

Teaching methods

Lectures
Seminars
Tutorials
Project work

Summary

The subject Mathematical Statistics follows up on probability theory. It uses tools of probability to present estimation of population parameters, hypothesis testing, modelling of technological processes with regression models and their assessment by correlation analysis. Multivariate regression is taught under the necessary theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables.

Compulsory literature:

JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7.

Recommended literature:

MONTGOMERY, D. C. Applied Statistics and Probability for Engineers. NY: Wiley, 2010. ISBN-13 978-1-1185-3971-2. SHESKIN, D. J. Handbook of Parametric and Nonparametric Statistical Procedures. NY: Chapman and Hall, 2003. ISBN 1-58488-440-1.

Way of continuous check of knowledge in the course of semester

Written exam. Tests. Project.

E-learning

E-learning: Integrovaný systém modulární počítačové výuky ekonomicko-technického zaměření (http://lms.vsb.cz): Vzdělávací modul 4 – Zlepšování procesů s využitím statistické analýzy, submodul Průzkumová analýza dat: Grafické nástroje (s. 3 – 21) Intervalové odhady (s. 25 – 33) Testování hypotéz (s. 33 – 67) Regresní analýza (s. 73 – 90) TOŠENOVSKÝ, J. Plánování experimentů. Studijní opory. Ostrava: VŠB-TU Ostrava, 2012. TOŠENOVSKÝ, J. Teorie pravděpodobnosti. Studijní opory. Ostrava: VŠB-TU Ostrava, 2012.

Other requirements

Submission of projects, the successful completion of tests during the semester, active participation in the lesson.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Population and sample, random sample, frequencies 2. Division of data into classes (procedure and reason for doing so), histogram 3. Moment and quantile characteristics 4. The theorem on a single drawing from normal distribution and its use 5. The theorem on two drawings from normal distribution and its use 6. Hypothesis testing – general procedure, type I and II errors in testing 7. F-test, t-tests (all steps taken in the test) 8. Correlation analysis (the r coefficient and its testing, correlation index, condition for use, properties) 9. Multivariate regression analysis (principal matrix formulae) 10. Spearmann’s correlation coefficient, contingency tables 11. Point estimation of 12. Interval estimation of 13. Test of normality (skewness and kurtosis of normal distribution, Shapiro-Wilk test and its table of critical values) 14. Testing of outliers (Grubb’s test, Box Plot), tests of data independence (sign test).

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
FMT+9360 2020/2021 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
FMT-new subjects 2019/2020 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block