Course detail

Statistics

FP-UstatlPAcad. year: 2017/2018

Random events: Probability and their properties, conditioned probability, classical probability, independed events, total probability.
Random variables: Random variables of discrete and continuous type, characteristics and distribution laws, distribution binomial, hypergeometric, geometric, Poisson, normal and exponential.
Mathematical Statistcs: Processing univariate sample data with a quantitative variable, points and intervals estimation of population parameters, testing statistical hypothesis.
Index Numbers: Simple and composite index numbers, Laspeyres and Paasche index numbers.
Regression Analysis: Method of least-squares, regression line, special regression function.
Time Series: Characteristics of time series, decomposition of time series, trend in a time series.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Learning outcomes of the course unit

Students will be made familiar with the fundamentals of random variables, mathematical statistics, analysis of index numbers, regression analysis and time series and will learn how to use its methods to solve economic problemes. After completion of this course students will be prepared to study economic topics working with uncertainty.

Prerequisites

Fundamentals of linear algebra and mathematical analysis.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course contains lectures that explain basic principles, problems and methodology of the discipline, and exercises that promote the practical knowledge of the subject presented in the lectures.

Assesment methods and criteria linked to learning outcomes

COURSE-UNIT CREDIT: The course-unit credit is awarded on the following conditions:
- participation in seminars,
- submitting answers to theoretical questions,
- submitting answers to elaboration calculating projects.

EXAM: The exam has a written form.
In the first part of the exam student solves examples within 60-70 minutes. (It is allowed to use recomended literature.)
In the second part of the exam student works out answers to theoretical questions within 15 minutes.
The mark, which corresponds to the total sum of points achieved (max 100 points), consists of:
- points achieved in control tests, achieved to calculating projects elaboration; these points must be achieved in the semestr, in which is examen.
- points achieved by solving examples,
- points achieved by answering theoretical questions.

The grades and corresponding points:
A (100-90), B (89-83), C (82-76), D (75-69), E (68-60), F (59-0).

Course curriculum

Random events.
Discrete random variables.
Continuous random variables.
Processing data samples.
Tests of statistical hypotheses.
Composite and aggregate index numbers.
Regression analysis.
Time series.

Work placements

Not applicable.

Aims

The objective of the course is to make students familiar with the fundamentals of random variables, mathematical statistics, analysis of index numbers, regression analysis and time series. They will be able to study economic topics working with uncertainty, and to solve problems related to these topics applying the methods of this theory.

Specification of controlled education, way of implementation and compensation for absences

Attendance at lectures is not compulsory, but is recommended. Attendance at exercises is required and checked by the tutor. An excused absence of a student from seminars can be compensated for by submitting solution of alternate exercises.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KROPÁČ, J. Statistika. 2. vyd. CERM, Brno. 2012. ISBN 978-80-7204-788-8. (CS)
SEGER, J. aj. Statistické metody v tržním hospodářství. Praha : Victoria Publishing, 1995. ISBN 80-7187-058-7. (CS)

Recommended reading

HINDLS, R. aj. Analýza dat v manažerském rozhodování. Praha : Grada Publishing, 1999. ISBN 80-7169-255-7. (CS)
SWOBODA, H. Moderní statistika. Praha : Svoboda, 1977. (CS)

Classification of course in study plans

  • Programme BAK Bachelor's

    branch BAK-UAD , 3 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

13 hod., optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

Random events.
Discrete random variables.
Continuous random variables.
Processing data samples.
Tests of statistical hypotheses.
Composite and aggregate index numbers.
Regression analysis.
Time series.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

1.Náhodný pokus, náhodný jev, operace s jevy, klasická a statistická definice pravděpodobnosti, pravidla pro počítání s pravděpodobnostmi
2. Podmíněná pravděpodobnost, nezávislost jevů.
3.Náhodné diskrétní a spojité veličiny, distribuční funkce, pravděpodobnostní funkce, hustota pravděpodobnosti, kvantily a jejich vlastnosti.
4. Charakteristiky náhodné veličiny - střední hodnota a rozptyl.
5.Diskrétní rozdělení - alternativní, binomické, Poissonovo, hypergeometrické. 6.Spojitá rozdělení - normální, lognormální, exponenciální. Speciální rozdělení - t, F, chí kvadrát. Centrální limitní věta, zákon velkých čísel.
7.Zpracování a vyhodnocování jednorozměrných datových souborů kvantitativního znaku.
8.Bodový odhad a jeho vlastnosti, bodový odhad střední hodnoty a rozptylu, intervalový odhad střední hodnoty a rozptylu.
9.Testování hypotéz. Obecný postup testování,jednovýběrový t-test
10. párový a dvouvýběrový t-test, F-test, Chí-kvadrát test dobré shody.
11.Jednoduchá lineární regrese.
12 Úvod do korelační analýzy.
13.Časové řady. Elementární charakteristiky časových řad, bazické a řetězové indexy, klasická dekompozice časové řad