714-0368/03 – Mathematics III (MIII)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorIng. Petra Schreiberová, Ph.D.Subject version guarantorIng. Petra Schreiberová, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
OTI73 Mgr. Petr Otipka
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

Teaching methods

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

Požadavky pro udělení zápočtu a zkoušky Cvičení: Podmínky pro udělení zápočtu (denní studium): - účast ve cvičení, 20 % neúčasti lze omluvit, - odevzdání programů zadaných vedoucím cvičení v předepsané úpravě, - absolvování 3 písemných testů (maximálně po 5 bodech). Za splnění podmínek získá student 5 b. Student, který získá zápočet, bude hodnocen 5 - 20 b. Zkouška Písemná část zkoušky bude hodnocena 0 - 60 b, za její úspěšné absolvování bude považován zisk 25 b. Ústní část zkoušky bude hodnocena 0 - 20 b, za její úspěšné absolvování bude považován zisk 5 b. Soubor otázek Jevy, jevová algebra Jevy neslučitelné, skupina vzájemně neslučitelných jevů Způsoby definice pravděpodobnosti Základní pravidla pro výpočet pravděpodobnosti Podmíněná a úplná pravděpodobnost Bayerův vzorec Náhodná veličina, náhodná proměnná Funkce používané k popisu náhodné proměnné Funkce rozložení pravděpodobnosti u diskrétní a spojité náhodné veličiny Vztah mezi frekvenční a distribuční funkci rozložení pravděpodobnosti Číselné charakteristiky náhodné veličiny Momentové charakteristiky náhodné veličiny Základní teoretická rozložení náhodné veličiny a jejich limitní tvary Vícerozměrná náhodná veličina, náhodný vektor Pravděpodobnostní funkce rozložení vícerozměrné náhodné veličiny Statistický soubor s jedním a s více argumenty Číselné charakteristiky statistického souboru jednorozměrného a vícerozměrného Regresní a korelační analýza Analýza časových řad, základní principy Statistická indukce, základní soubor, výběrový soubor, parametry, charakteristiky Odhady parametrů základního souboru (pro střední hodnotu a rozptyl) Statistické hypotézy, druhy statistických hypotéz Nulová hypotéza, alternativní hypotézy (jednostranné a oboustranné testy) Standardní postup u testování statistických hypotéz Interpretace výsledku testu statistické hypotézy Požaduje se znalost základních statistických výpočtů v MS Excelu

E-learning

Další požadavky na studenta

There are no more requirements.

Prerequisities

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

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus of lectures and tutorials ========================= 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. 11. Time series. 12. Forecasting. Time series methods.

Conditions for subject completion

Full-time form (validity from: 2014/2015 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20  5
        Examination Examination 80 (80) 31
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2018/2019 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2018/2019 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2018/2019 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2017/2018 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2017/2018 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2017/2018 (B3712) Air Transport Technology (3708R038) Aircraft Maintenance Technology P Czech Ostrava 2 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2016/2017 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2016/2017 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 2 Compulsory study plan
2016/2017 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2015/2016 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2015/2016 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 2 Compulsory study plan
2014/2015 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2014/2015 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2014/2015 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2013/2014 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Šumperk 2 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 2 Compulsory study plan
2013/2014 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2012/2013 (B3712) Air Transport Technology (3708R037) Aircraft Operation Technology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B3712) Air Transport Technology (3708R036) Air Operation Technology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Šumperk 2 Compulsory study plan
2011/2012 (B2341) Engineering P Czech Ostrava 2 Compulsory study plan
2011/2012 (B2341) Engineering P Czech Šumperk 2 Compulsory study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology 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 2017/2018 Full-time Czech Optional FS - Faculty of Mechanical Engineering stu. block