# 310-2121/01 – Mathematics III (MIII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Ing. Petra Schreiberová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester winter Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
OTI73 Mgr. Petr Otipka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
SKN002 Ing. Petra Schreiberová, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

The goal of the course is to serve as a theoretical and practical base to understand the importance of the basic notions in probability, and teach the student statistical way of thinking as a mean of understanding real life processes, introduce basic methods of collecting and analysing statistical data, and show the student how to use these general methods in other courses of study and in professional career. The graduate of this course should be able: • understand and use basic notions in combinatorics and probability theory • formulate questions, which can be answered based on the given data, for this purpose learn the principles of collecting, processing data and presentation of relevant values and results • choose and use suitable statistical methods for data analysis • suggest and evaluate conclusions (inference) and predictions obtained from data

Lectures
Seminars
Tutorials
Project work
Other activities

### Summary

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.Estimating of parameters of population. Testing of hypotheses. Exercises - EXCEL.

### Compulsory literature:

Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005. ISBN 80-248-0803-X.

### Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1. James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6.

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

Zápočet - odevzdání programu - absolvování 2 písemných testů Zkouška - kombinovaná Nutnou podmínkou pro absolvování zkoušky je uzavření předmětu Matematika II.

### E-learning

http://mdg.vsb.cz/portal/m3/index.php

### Other requirements

There are no more requirements.

### Prerequisities

Subject codeAbbreviationTitleRequirement
310-2112 MII Mathematics II Compulsory
310-2117 M1 Mathematics 1 Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Combinatorics. Random events, operations with them, sample space. 2. Definitions of probability events - classical, geometrical, statistics. Conditional probability, Bayes\' theorem. Bernoulli independent repeated trials. 3. Discrete random variable and continuous random variable. Functions of random variables. Moment generating function, quantiles. 4. Discrete probability distribution. 5. Continuous probability distribution. 6. Random vector. The probability distribution. Expected value, covariance, coefficient of correlation. 7. Statistics. Statistical methods, descriptive statistics 8. Observed data. Point estimators, interval estimators. 9. Statistical hypothesis testing – the testing process, interpretation, importance. Parametric and non-parametric tests. 10. Correlation and regression analysis.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30 3
Praktická část Written examination 60  25
Teoretická část Oral examination 20  5
Mandatory attendence participation: 80 %

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B0713A070002) Energetics and Environments P Czech Ostrava 2 Compulsory study plan
2023/2024 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 2 Compulsory study plan
2023/2024 (B0715A270011) Engineering P Czech Ostrava 2 Compulsory study plan
2023/2024 (B0715A270011) Engineering P Czech Šumperk 2 Compulsory study plan
2022/2023 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 2 Compulsory study plan
2022/2023 (B0713A070002) Energetics and Environments P Czech Ostrava 2 Compulsory study plan
2022/2023 (B0715A270011) Engineering P Czech Ostrava 2 Compulsory study plan
2022/2023 (B0715A270011) Engineering P Czech Šumperk 2 Compulsory study plan
2022/2023 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2022/2023 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2022/2023 (B1088A040001) Operation and management of air transport (S01) Air Transport Technology and Management P Czech Ostrava 2 Compulsory study plan
2022/2023 (B1088A040001) Operation and management of air transport (S02) Aviation Operation Management P Czech Ostrava 2 Compulsory study plan
2021/2022 (B0715A270011) Engineering P Czech Ostrava 2 Compulsory study plan
2021/2022 (B0715A270011) Engineering P Czech Šumperk 2 Compulsory study plan
2021/2022 (B0713A070002) Energetics and Environments P Czech Ostrava 2 Compulsory study plan
2021/2022 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 2 Compulsory study plan
2021/2022 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2021/2022 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2020/2021 (B0715A270011) Engineering P Czech Ostrava 2 Compulsory study plan
2020/2021 (B0715A270011) Engineering P Czech Šumperk 2 Compulsory study plan
2020/2021 (B0713A070002) Energetics and Environments P Czech Ostrava 2 Compulsory study plan
2020/2021 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 2 Compulsory study plan
2020/2021 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2020/2021 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2020/2021 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2020/2021 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2020/2021 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2019/2020 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2019/2020 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2019/2020 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2019/2020 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2019/2020 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2019/2020 (B0713A070002) Energetics and Environments P Czech Ostrava 2 Compulsory study plan
2019/2020 (B0715A270011) Engineering P Czech Ostrava 2 Compulsory study plan
2019/2020 (B0715A270011) Engineering P Czech Šumperk 2 Compulsory study plan
2019/2020 (B0715A040001) Transport Systems and Equipment P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FS - P - cs 2021/2022 Full-time Czech Optional FS - Faculty of Mechanical Engineering stu. block