# 714-0368/02 – Mathematics III (MIII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Fiktivní Uživatel Study level undergraduate or graduate Study language Czech Year of introduction 1999/2000 Year of cancellation 2008/2009 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
HOM44 PaedDr. Zdenka Homolová
NIK01 Ing. Marek Nikodým, Ph.D.
OTI73 Mgr. Petr Otipka
STR78 Mgr. Jakub Stryja, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 12+4

### 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

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0366 MI Mathematics I Compulsory
714-0367 MII Mathematics II Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Program přednášek ================= I. Pravděpodobnost -------------------- Kombinatorika. Náhodné jevy, operace s nimi, pojem neslučitelnosti a úplnosti, jevové pole. Definice pravděpodobnosti jevů - klasická, geometrická, statistická. Podmíněná pravděpodobnost. Úplná pravděpodobnost. Bernoulliho posloupnost nezávislých jevů. II. Náhodná veličina diskrétní a spojitá. ------------------------------------------ Frekvenční a distribuční funkce. Charakteristiky náhodných veličin. Základní typy rozdělení pravděpodobnosti diskrétní náhodné veličiny. Základní typy rozdělení pravděpodobnosti spojité náhodné veličiny. Náhodný vektor, rozdělení pravděpodobnosti, číselné charakteristiky. III. Statistika ---------------- Zpracování statistického souboru. Náhodný výběr, bodové a intervalové odhady. Testování hypotéz - testy parametrické a neparametrické. Lineární regrese. Časové řady - složka trendová, sezónní a náhodná. Prognózování. Program seminářů + individuální práce studentů ============================================== I. Výpočet pravděpodobnosti. II. Zpracování statistického souboru. Individuální práce studentů =========================== 1 semestrální úloha - počet pravděpodobnosti (3 h ) 1 semestrální úloha - zpracování datového souboru (3 h )

### Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 0
Examination Examination 80 (80) 0
Written examination Written examination 60  0
Oral Oral examination 20  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Třinec 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3907R004) Energy Management K Czech Třinec 2 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R007) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Třinec 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3901R003) Applied Mechanics K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Šumperk 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Třinec 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment K Czech Šumperk 2 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3907R004) Energy Management K Czech Třinec 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R007) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment K Czech Třinec 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Třinec 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3901R003) Applied Mechanics K Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R002) Transport Equipment K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3907R004) Energy Management K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R013) Robotics (70) Robotics K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R007) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R003) Transport Machinery and Material Handling K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3901R003) Applied Mechanics K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Ostrava 2 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 2 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner