| Course Unit Code | 310-2121/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 310-2112 | Mathematics II |
| 310-2117 | Mathematics 1 |
| Name of Lecturer(s) | Personal ID | Name |
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| OTI73 | Mgr. Petr Otipka, Ph.D. |
| SKN002 | Ing. Petra Schreiberová, Ph.D. |
| Summary |
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Probabilities of random events: axioms of probability, conditional probability,
independence. Random variables: discrete random variables, continuous random
variables, expected values. Important practical distributions of discrete and
continuous random variables.Estimating of parameters of population. Testing of
hypotheses. Exercises - EXCEL. |
| Learning Outcomes of the Course Unit |
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The goal of the course is to serve as a theoretical and practical base to understand the importance of the basic notions in probability, and teach the student statistical way of thinking as a mean of understanding real life processes, introduce basic methods of collecting and analysing statistical data, and show the student how to use these general methods in other courses of study and in professional career.
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
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| Course Contents |
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1. Combinatorics. Random events, operations with them, sample space.
2. Definitions of probability events - classical, geometrical, statistics.
3. Conditional probability, Bayes\' theorem. Bernoulli independent repeated trials.
4. Discrete random variable. Functions of random variables. Moment generating function.
5. Continuous random variable. Functions of random variables. Moment generating function, quantiles.
6. Discrete probability distribution.
7. Continuous probability distribution.
8. Statistics. Statistical methods, descriptive statistics
9. Interval estimators.
10. Statistical hypothesis testing – the testing process, interpretation, importance. Parametric tests.
11. Correlation and regression analysis. |
| Recommended or Required Reading |
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| Required Reading: |
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Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005.
ISBN 80-248-0803-X. |
Otipka, P.-Šmajstrla, V.: Pravděpodobnost a statistika. Skriptum VŠB-TU, Ostrava 2006. ISBN 80-248-1194-4.
Pavelka, L.-Doležalová, J.: Pravděpodobnost a statistika. Skriptum VŠB-TU, Ostrava 2003. ISBN 80-7078-976-X.
Dubovský, V., Jarošová, M., Krček, J., Krčková, J., Schreiberová, P., Volný, P.: Matematika III: Pracovní listy. 2015. ISBN 978-80-248-3875-5.
Schreiberová, P., Rabasová, M.: Workbook for Statistics. Skriptum VŠB-TUO, Ostrava 2021. ISBN 978-80-248-4490-9. http://mdg.vsb.cz/portal/en/Statistics_workbook.pdf |
| Recommended Reading: |
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Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1.
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993.
ISBN 0-201-56519-6. |
Hradecký, P. a kol.: Pravděpodobnost. Skriptum VŠB-TU, Ostrava 1998. ISBN 80-7078-442-3.
Hendl, J.: Přehled statistických metod zpracování dat. Praha : Portál, 2004. ISBN 80-7178-820-1.
http://mdg.vsb.cz/portal/m3/ |
| Planned learning activities and teaching methods |
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| Lectures, Seminars, Tutorials, Project work, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 5 |
| Examination | Examination | 80 (80) | 30 |
| Praktická část | Written examination | 60 | 25 |
| Teoretická část | Oral examination | 20 | 5 |