# 714-0368/01 – Mathematics III (MIII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Mgr. Petr Otipka, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester summer 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, Ph.D.
PRA76 Ing. Pavel Praks, Ph.D.
RYH40 RNDr. Irena Rychtarová
STR78 Mgr. Jakub Stryja, 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
Part-time 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 ================= Náplň přednášek ------------------------------------------------------------------------------- 1 Kombinatorika. Náhodné jevy, operace s nimi, pojem neslučitelnosti a úplnosti, jevové pole. 2 Definice pravděpodobnosti jevů - klasická, geometrická, statistická. Podmíněná pravděpodobnost. Úplná pravděpodobnost. Bernoulliho posloupnost nezávislých jevů. 3 Náhodná veličina diskrétní a spojitá. Frekvenční a distribuční funkce.Charakteristiky náhodných veličin. 4 Základní typy rozdělení pravděpodobnosti diskrétní náhodné veličiny. 5 Základní typy rozdělení pravděpodobnosti spojité náhodné veličiny. 6 Náhodný vektor, rozdělení pravděpodobnosti, číselné charakteristiky. 7 Zpracování statistického souboru. 8 Náhodný výběr, bodové a intervalové odhady 9 Testování hypotéz - testy parametrické. 10 Testování hypotéz - testy neparametrické. 11 Lineární regrese. 12 Časové řady - složka trendová, sezónní a náhodná. 13 Prognózování. Program cvičení a seminářů + individuální práce studentů ======================================================== Náplň cvičení a seminářů ------------------------------------------------------------------------------- 1 Kombinatorika - kombinace, variace a permutace bez opakování a s opakováním, jevové pole. 2 Výpočet pravděpodobnosti. 3 První test - pravděpodobnost. Náhodná veličina - určování frekvenční a distribuční funkce, výpočet charakteristik. 4 Rozdělení alternativní, binomické, hypergeometrické, Poissonovo. 5 Rozdělení rovnoměrné, exponenciální, normální, Weibullovo. 6 Druhý test - náhodná veličina. Náhodný vektor - podmíněná rozdělení, charakteristiky. 7 Zpracování statistického souboru. 8 Zpracování statistického souboru - program. 9 Odhady parametrů základního souboru. 10 Testování hypotéz - hypotézy o střední hodnotě a rozptylu, testy shody. 11 Jednoduchá lineární regrese. 12 Časové řady - trendová, sezónní, náhodná složka, prognózování. 13 Třetí test - zpracování statistického souboru.

### Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
Exercises evaluation Credit 20 (20) 0 3
Examination Examination 80 (80) 0 3
Written examination Written examination 60  0 3
Oral Oral examination 20  0 3
Mandatory attendence participation:

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

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### Occurrence in study plans

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2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
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2006/2007 (B2341) Engineering (2301R013) Robotics (71) P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (71) K Czech Ostrava 2 Compulsory study plan
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2005/2006 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Compulsory study plan
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2005/2006 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
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2005/2006 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P 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 P Czech Ostrava 2 Compulsory study plan
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2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P 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 P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

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