# 714-0086/02 – Statistics (S)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 3 Subject guarantor doc. RNDr. Zdeněk Boháč, CSc. Subject version guarantor doc. RNDr. Zdeněk Boháč, CSc. Study level undergraduate or graduate Requirement Compulsory Year 3 Semester winter Study language Czech Year of introduction 2002/2003 Year of cancellation Intended for the faculties FBI Intended for study types Bachelor
Instruction secured by
BOH10 doc. RNDr. Zdeněk Boháč, CSc.
KOL70 doc. Dr. Mgr. Ivan Kolomazník
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 16+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

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Random variables: Discrete and continuous random variables, probability distribution, density function, mean, variance, standard deviation. Characteristics of population and sample, measures of central tendency, measures of dispersion sampling distributions. Point estimates, confidence interval, testing hypotheses.

### Compulsory literature:

[1] Triola, Mario, F.: Elementary Statistics. Benjamin/Cummings Publ. Comp., Inc., Redwood City, California 1989. [2] Boháč, Z.: Numerical Methods and Statistics. VŠB – TUO, Ostrava 2005. ISBN 80-248-0803-X

### Recommended literature:

[1] Buchanan, James., L.,Turner, Peter., R.: Numerical Methods and Analysis. McGraw-Hill, Inc. New York 1992. ISBN 0-07-008717-2

### Way of continuous check of knowledge in the course of semester

Podmínky pro udělení zápočtu (kombinované studium) Za zápočet lze získat maximálně 20 bodů, body lze získat dvěma způsoby: - při alespoň 50% účasti na konzultacích; za 50% účast lze získat 10 bodů, při 100% účasti 20 bodů, jinak přiměřený počet bodů podle účasti (lineární interpolací), - při menší než 50% účasti; odevzdání elaborátu s řešením 10 příkladů uvedených na homen.vsb.cz/~boh10/ lze získat 5 bodů. Za zápočet je možno získat celkem 5-20 bodů. Požadavky ke zkoušce: - zkouška se skládá z části písemné (příklady) a části ústní (teoretické), - v části písemná se řeší pět příkladů, maximální počet bodů 60, minimální nutný bodový zisk je 25 bodů, - část ústní (teoretická), zkouší se teorie v odpřednášeném rozsahu, maximální počet bodů 20, minimální nutný bodový zisk je 5 bodů. Společně se zápočtem lze získat celkem 100 bodů. Podmínkou pro účast na zkoušce je zápočet zapsaný ve Výkazu o studiu. Klasifikace: 100-86 výborně, 85-66 velmi dobře, 65-51 dobře, 50-0 nevyhověl. Soubor otázek k teoretické části zkoušky: 1. Náhodný pokus a náhodný jev, definice pravděpodobnosti. 2. Nezávislé jevy a jejich pravděpodobnost. 3. Diskrétní náhodná veličina, zákon rozdělení pravděpodobnosti a distribuční funkce. 4. Spojitá náhodná veličina, funkce hustoty a distribuční funkce. 5. Číselné charakteristiky rozdělení náhodné veličiny. 5. Rozdělení diskrétní náhodné veličiny (alternativní, binomické, Poissonovo). 7. Rozdělení spojité náhodné veličiny (rovnoměrné, exponenciální, normální). 8. Statistický soubor, variační řada, třídní rozdělení četností. 9. Základní soubor a jeho parametry, náhodný výběr a jeho empirické charakteristiky. 10. Bodové a intervalové odhady parametrů. 11. Momentová metoda a metoda maximální věrohodnosti. 12. Testování hypotéz. 13. Test významnosti rozdílu dvou rozptylů (F-test). 14. Test významnosti rozdílu |M-mi|. 15. Test významnosti dvou výběrových průměrů (t-test). 16. Test významnosti rozdílu párovaných hodnot. 17. Testy dobré shody.

### E-learning

www.studopory.vsb.cz mdg.vsb.cz

No more requirements are put on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Random event, experiment, definition of probability, conditional probability, independent events and its probability. Random variable. Discrete random variable, probability function, distribution function of a discrete random variable. Numerical chracteristics. Discrete uniform distribution, Poisson distribution, binomial distribution, hypergeometric distribution. Continuous random variable. Probability density function, distribution function of a continuous random variable. Numerical characteristics. Uniform distribution, exponential distribution, normal distribution. Population. Data sample, frequency distributions. Random sample and empirical characteristics. Point and interval estimates of parameters, method of moments and maximum likelihood method. Correlation and regression analysis, covariant and correlation matrix. Approximation by the method of least squares. Tests of hypotheses. F-test of the equality of two variances, unpaired and paired two-sample t-tests, Kolmogorov–Smirnov test, two-sample Kolmogorov–Smirnov test, Dixon's Q test, Grubbs' test for outliers.

### Conditions for subject completion

Part-time form (validity from: 2014/2015 Winter semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 5
Jiný typ úlohy Other task type 20  5
Examination Examination 80 (80) 30
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.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Lázně Bohdaneč 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Lázně Bohdaneč 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2017/2018 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Lázně Bohdaneč 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Lázně Bohdaneč 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2016/2017 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2015/2016 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Lázně Bohdaneč 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Lázně Bohdaneč 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Lázně Bohdaneč 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2014/2015 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2013/2014 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Příbram 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Příbram 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Lázně Bohdaneč 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2012/2013 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Příbram 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2011/2012 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Most 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Příbram 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Příbram 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Příbram 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2010/2011 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Most 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Most 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2009/2010 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Most 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Most 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Most 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Most 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Most 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Liberec 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Most 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Liberec 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 3 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 3 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 3 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Praha 3 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 3 Compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R005) Engineering Safety of Persons and Property K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R006) Fire Protection Engineering and Industrial Safety K Czech Ostrava 2 Optional study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R001) Occupational and Process Safety K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management K Czech Ostrava 2 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner