714-0368/04 – Mathematics III (MIII)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorIng. Petra Schreiberová, Ph.D.Subject version guarantorMgr. Petr Otipka
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction2010/2011Year of cancellation2019/2020
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
OTI73 Mgr. Petr Otipka
SKN002 Ing. Petra Schreiberová, 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

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 Zápočet: Podmínky pro udělení zápočtu: Za účast na konzultacích může student získat 5 - 20 b, v případě neúčasti může student získat 5 b za zpracování zadaného programu. Kombinovaná zkouška: Podmínkou pro účast na zkoušce je zapsaný zápočet z příslušného předmětu. 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.

E-learning

Další požadavky na studenta

Syllabus of lectures ================= I. Probability -------------------- Combinatorics. Random events, operations with them, sample space. Definitions of probability events - classical, geometrical, statistics. Conditional probability, Bayes' theorem. Bernoulli independent repeated trials. II. Discrete random variable and continuous random variable. ---------------------------------------------------------------------------------------- Functions of random variables. Moment-generating function, quantiles. Discrete probability distribution. Continuous probability distribution. Random vector. The probability distribution. Expected value, covariance, coefficient of correlation. III. Statistics. Statistical methods, descriptive statistics Observed data. Point estimators, interval estimators. Statistical hypothesis testing – the testing process, interpretation, importance. Parametric and non-parametric tests. Correlation and regression analysis. Time series. Forecasting. Time series methods.

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 ================= I. Probability -------------------- Combinatorics. Random events, operations with them, sample space. Definitions of probability events - classical, geometrical, statistics. Conditional probability, Bayes' theorem. Bernoulli independent repeated trials. II. Discrete random variable and continuous random variable. ---------------------------------------------------------------------------------------- Functions of random variables. Moment-generating function, quantiles. Discrete probability distribution. Continuous probability distribution. Random vector. The probability distribution. Expected value, covariance, coefficient of correlation. III. Statistics. Statistical methods, descriptive statistics Observed data. Point estimators, interval estimators. Statistical hypothesis testing – the testing process, interpretation, importance. Parametric and non-parametric tests. Correlation and regression analysis. Time series. Forecasting. Time series methods.

Conditions for subject completion

Combined form (validity from: 2010/2011 Winter semester, validity until: 2013/2014 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 (20) 5
                Other task type Other task type 20  5
        Examination Examination 80 (80) 30
                Written examination Written examination 60  25
                Oral 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 K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2018/2019 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2018/2019 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2017/2018 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2017/2018 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2016/2017 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2016/2017 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2015/2016 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2015/2016 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2014/2015 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2014/2015 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2014/2015 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2013/2014 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Šumperk 2 Compulsory study plan
2013/2014 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2012/2013 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Šumperk 2 Compulsory study plan
2012/2013 (B2341) Engineering (2302R010) Design of Machines and Equipment (50) Hunting, Sporting, Defense Arms and Ammunition K Czech Uherský Brod 2 Compulsory study plan
2011/2012 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2011/2012 (B2341) Engineering K 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 - K - cs 2017/2018 Combined Czech Optional FS - Faculty of Mechanical Engineering stu. block