# ESF:BKM_STA1 Statistics I - Course Information

## BKM_STA1 Statistics I

**Faculty of Economics and Administration**

Autumn 2023

**Extent and Intensity**- 26/0/0. 5 credit(s). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- Mgr. Lenka Zavadilová, Ph.D. (lecturer)

Mgr. Terézia Černá (seminar tutor)

Ing. Mgr. Vlastimil Reichel, Ph.D. (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 13 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**- 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

*required 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

*recommended literature*- BUDÍKOVÁ, Marie, Maria KRÁLOVÁ and Bohumil MAROŠ.
**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)**- 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****BKM_STA2**Statistics 2

(BKM_STA1) || (BPM_STA1) && forma(K)

- Enrolment Statistics (recent)

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