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Stochastic Methods of Modelling

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-3241/01
Number of ECTS Credits Allocated3 ECTS credits
Type of Course Unit *Choice-compulsory type B
Level of Course Unit *Second Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KAH14Mgr. Marcela Rabasová, Ph.D.
Summary
Combinatorics and probability. Random events, operations with them, sample space.
Definitions of events' probability - classical, geometrical, statistics. Conditional probability. Total probability and independent events.
Random variable and its characteristics.
Basic types of probability distributions of discrete random variables.
Basic types of probability distributions of continuous random variables.
Random vector, probability distribution, numerical characteristics.
Statistical file with one factor. Grouped frequency distribution.
Statistical file with two factors.
Regression and correlation.
Random sample, point and interval estimations of parameters.
Hypothesis testing.
Learning Outcomes of the Course Unit
The aim of the course is to provide theoretical and practical foundation for understanding the importance of basic probability concepts and teach the student statistical thinking as a way of understanding the processes and events around us, to acquaint him with the basic methods of gathering and analyzing statistical data, and to show how to use these general procedures in other subjects of study and in practice.

Graduates of this course should be able to:
• understand and use the basic terms from the combinatorics and probability theory;
• formulate questions that can be answered by the data and understand principles of collecting, processing and presentation of the data;
• select and use appropriate statistical methods for data analysis;
• propose and evaluate conclusions (inference) and make predictions using the data.


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
Course Contents
1. Combinatorics
2. Introduction to probability
3. Conditional probability and independent events. Bayes' theorem. Theorem of total probability.
4. Random variable and its characteristics
5.-7. The basic distributions of discrete and continuous random variable
8. Statistical file with one factor
9. Regression and correlation
10. Point and interval estimates of parameters
11.-12. Hypothesis testing
13. Reserve
Recommended or Required Reading
Required Reading:
Dummer R. M.: INTRODUCTION TO STATISTICAL SCIENCE. VŠB-TU Ostrava 1998; ISBN 80-7078-497-0
Otipka P., Šmajstrla V.: Pravděpodobnost a statistika. VŠB-TU Ostrava 2012;
http://www.studopory.vsb.cz/materialy.html
Recommended Reading:
Dummer R. M.: INTRODUCTION TO STATISTICAL SCIENCE. VŠB-TU Ostrava 1998; ISBN 80-7078-497-0
M. Litschmannová: Vybrané kapitoly z pravděpodobnosti. FEI VŠB TU Ostrava 2011; http://mi21.vsb.cz/modul/vybrane-kapitoly-z-pravdepodobnosti

M. Litschmannová: Úvod do statistiky. FEI VŠB TU Ostrava 2011; http://mi21.vsb.cz/modul/uvod-do-statistiky

Pavelka L., Doležalová J.: Pravděpodobnost a statistika. VŠB-TU Ostrava 1999; ISBN 80-7078-976-X
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21