714-0589/01 – Stochastic Methods of Modelling (S)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Mgr. Marcela Rabasová, Ph.D. | Subject version guarantor | Mgr. Marcela Rabasová, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2019/2020 |
| Intended for the faculties | HGF, USP | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
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.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Two tests, 1 project - data analysis.
E-learning
http://stattrek.com/tutorials/statistics-tutorial.aspx
Other requirements
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Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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. Random vector
9. Statistical file with one factor
10. Statistical file with two factors
11. Regression and correlation
12. Point and interval estimates of parameters
13. Hypothesis testing
14. Reserve
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction