# 310-2121/02 – Mathematics III (MIII)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Ing. Petra Schreiberová, Ph.D. Subject version guarantor Mgr. Petr Otipka Study level undergraduate or graduate Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS Intended for study types Bachelor
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+0

### 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: Za účast na konzultacích může student získat 5 - 20 b, v případě neúčasti může student získat 5 b za zpracování zadaného programu. Kombinovaná 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. 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

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

### Další požadavky na studenta

no further requirements

### Prerequisities

Subject codeAbbreviationTitleRequirement
310-2111 MI Mathematics I Compulsory
310-2112 MII Mathematics II Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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.

### Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2341) Engineering K Czech Ostrava 2 Compulsory study plan
2019/2020 (B2341) Engineering K Czech Šumperk 2 Compulsory study plan
2019/2020 (B2341) Engineering (2301R003) Transport Equipment and Technology K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner