## BKM_STA1 Statistics I

Autumn 2020
Extent and Intensity
26/0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Terézia Černá (seminar tutor)
Ing. Mgr. Vlastimil Reichel (seminar tutor)
RNDr. Marie Budíková, Dr. (alternate examiner)
Guaranteed by
doc. Mgr. Maria Králová, Ph.D.
Department of Applied Mathematics and Computer Science - Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science - Faculty of Economics and Administration
Prerequisites (in Czech)
( BKM_MATE Mathematics ) || ( BPM_MATE Mathematics )
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 18 fields of study the course is directly associated with, display
Course objectives
The course consists of descriptive statistics and principles of probability theory. The tutorials include motivation of the elementary concepts, key statements and calculation of typical examples. The topics follow a fixed procedure: descriptive statistical characteristics of nominal, ordinal, interval and proportional indicators; regression line; the basic properties of probability, stochastic independence of phenomena, conditional probability; random variables and vectors, their discrete and continuous type; joint distribution and stochastic independence of random variables; characteristics of random variables; asymptotic expressions; normal and other exact distributions.

At the end of this course, students should be able to:
understand terms from probability and statistics; correctly present real data; apply basics of probability to simple real situations.
Learning outcomes
After graduation of the course student should be able to:
- use and interpret functional and numeric characteristics within a framework of descriptive statistics
- describe types of variables with respect to measurement scale
- quantify randomness in elementary setting by probability
- use and properly interpret distributional function, probability function and density function
- determine in mathematical statistics popular distributions with respect to the application context
Syllabus
• 1. Frequency and probability, properties of probability, examples.
• 2. Independent events, properties of independent events, sequence of independent events.
• 3. Conditional probability, total probability rule, examples.
• 4. Prior and posterior probabilities, Bayes' theorem, examples.
• 5. Descriptive statistics, quantitative variables, qualitative variables; frequency distributions in tables and graphs, examples of data sets.
• 6. Functional characteristics and numerical descriptive measures for univariate and multivariate quantitative variables, examples.
• 7. Random variable, distribution function and its properties, discrete and continous variable, transformation of random variable.
• 8. Discrete probability distribution, probability function and its properties; continuous probability distribution, probability density and its properties; random vector and its functional characteristics.
• 9. Simultaneous and marginal random vectors, independent random variables, sequence of Bernoulli trials.
• 10. Examples of discrete and continuous probability distributions and their application in the field of economics.
• 11. Numerical measures of probability distribution: expected value, variance, quantile, their properties and application in economics.
• 12. Numerical measures of simultaneous probability distribution: covariance, correlation coefficient, their properties and application in economics.
• 13. Characteristics of random vectors, inequality theorems (Markov inequality theorem, Cebysev inequality theorem).
Literature
required literature
• BUDÍKOVÁ, Marie, Maria KRÁLOVÁ and Bohumil MAROŠ. Průvodce základními statistickými metodami (Guide to basic statistical methods). vydání první. Praha: Grada Publishing, a.s., 2010. 272 pp. edice Expert. ISBN 978-80-247-3243-5. URL info
recommended literature
• BUDÍKOVÁ, Marie. Statistika. 1. vyd. Brno: Masarykova univerzita v Brně, 2004. 186 s. ISBN 8021034114. info
• BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika (Descriptive Staistics). 2. dotisk 3. vydání. Brno: Masarykova univerzita v Brně, 2002. 52 pp. ISBN 80-210-1831-3. info
• BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika.Sbírka příkladů. (Probability Theory and Mathematical Statistics.Collection of Tasks.). 2.dotisk 2.přeprac.vyd. Brno: Masarykova univerzita Brno, 2002. 127 pp. ISBN 80-210-1832-1. info
• BUDÍKOVÁ, Marie, Tomáš LERCH and Štěpán MIKOLÁŠ. Základní statistické metody. 1. vyd. Brno: Masarykova univerzita, 2005. 170 pp. ISBN 978-80-210-3886-8. info
• Elementární statistická analýza. Edited by Lubomír Cyhelský - Jana Kahounová - Richard Hindls. 2. dopl. vyd. Praha: Management Press, 2001. 318 s. ISBN 80-7261-003-1. info
Teaching methods
Distance study: lectures, self study.
Assessment methods
Written exam consisting of theoretical and practical parts, POT (final project corrected by tutor).
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is taught: in blocks.
Note related to how often the course is taught: 12 hodin.
Information on the extent and intensity of the course: tutorial 12 hodin.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019.
• Enrolment Statistics (recent)