639-2002/04 – Mathematical Statistics (MS)
| Gurantor department | Department of Quality Management | Credits | 7 |
| Subject guarantor | Ing. Filip Tošenovský, Ph.D. | Subject version guarantor | Ing. Filip Tošenovský, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Bachelor |
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:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Two tests in the course of the semester, where the score is counted towards the cumulative credit points.
One project, where the score is counted towards the cumulative credit points.
The examination is in written form.
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction