# 714-0268/06 – Mathematics III (BcM3)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor Mgr. Jitka Krčková, Ph.D. Subject version guarantor Mgr. Jitka Krčková, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 2014/2015 Year of cancellation 2019/2020 Intended for the faculties FAST Intended for study types Bachelor
Instruction secured by
DUB02 RNDr. Viktor Dubovský, Ph.D.
JAR71 Mgr. Marcela Jarošová, Ph.D.
KRC76 Mgr. Jiří Krček
KRC23 Mgr. Jitka Krčková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 16+0

### Subject aims expressed by acquired skills and competences

The aim of the course is to provide theoretical and practical foundation for understanding of the meaning of basic probability terms and teach the student to statistical thinking as a way of understanding of the processes and events around us, to acquaint him with the basic methods of statistical data gathering and analyzing, and to show how to use these general procedures in other subjects of study and in practice. Graduates of this course should be able to: • understand and use the basic terms of combinatorics and probability theory; • formulate questions that can be answered by the data, learn the principles of data collecting, processing and presenting; • select and use appropriate statistical methods for data analysis; • propose and evaluate conclusions (inferences) and predictions using the data.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Combinatorics and probability. Random events, operations with them, sample space. Definitions of events' probability - classical, geometrical, statistics. Conditional probability. Total probability and independent events. Random variable and its characteristics. Basic types of probability distributions of discrete random variables. Basic types of probability distributions of continuous random variables. Random vector, probability distribution, numerical characteristics. Statistical file with one factor. Grouped frequency distribution. Statistical file with two factors. Regression and correlation. Random sample, point and interval estimations of parameters. Hypothesis testing.iables: two-dimensional integrals, three-dimensional integrals, line integral of the first and the second kind. Probabilities of random events: axioms of probability, conditional probability, independence. Random variables: discrete random variables, continuous random variables, expected values. Important practical distributions of discrete and continuous random variables.

### Compulsory literature:

Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

### Recommended literature:

Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

### Way of continuous check of knowledge in the course of semester

Passing the course, requirements Course-credit -participation on tutorials is obligatory, -elaborate programs, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 86 85 - 66 65 - 51 50 - 0 National grading scheme excellent very good satisfactory failed 1 2 3 4 List of theoretical questions: 1. Combinatorics. 2. Random events. 3. Probabilities of random events - clasical, geometrical, statistical. 4. Conditional probability. 5. Composite probability. 6. Bernoulli sequence of independent random trials. 7. Bayes formula. 8. Discrete random variable. 9. Continuous random variable. 10. Probability mass and density function. Probability distribution funciton. 11. Characteristics of random variables. 12. Basic types of probability distributions of discrete random variables. 13. Basic types of probability distributions of continuous random variables. 14. Random vectors, their probabilities distribution and characteristics. 15. Processing of the statistical sample. 16. Random selection. 17. Point estimates. 18. Interval estimates. 19. Testing of hypothesis, parametrical tests. 20. Testing of hypothesis, nonparametrical tests. 21. Linear regression. 22. Least square method.

### E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz (in Czech language)

### Other requirements

http://www.studopory.vsb.cz http://mdg.vsb.cz (in Czech language)

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0267 BcM2 Mathematics II Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Syllabus of lecture Combinatorics. Random events and their operations. Probabilities of random events - clasical, geometrical, statistical. Conditional probability. Composite probability. Bernoulli sequence of independent random trials. Bayes formula. Discrete and continuous random variable. Probability mass and density function. Probability distribution funciton. Characteristics of random variables. Basic types of probability distributions of discrete and continuous random variables. Random vectors, their probabilities distribution and characteristics. Processing of the statistical sample. Random selection, point and interval estimates. Testing of hypothesis - parametrical and nonparametrical tests. Linear regression. Least square method.

### Conditions for subject completion

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

### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (B3607) Civil Engineering K Czech Ostrava 2 Compulsory study plan
2016/2017 (B3607) Civil Engineering K Czech Ostrava 2 Compulsory study plan
2015/2016 (B3607) Civil Engineering K Czech Ostrava 2 Compulsory study plan
2014/2015 (B3607) Civil Engineering K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner