MA0008 Theory of Probability

Faculty of Education
Spring 2025
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Mgr. Helena Durnová, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Helena Durnová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
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
Course objectives
In the course, the student learns the basics of probability theory. At the end of the course, the student will have learnt to distinguish statistical and classical definition of probability and will know the formulas that allow us compute the probability of various phenomena. The students will also learn basic ways of treating random variable and the basic methods of describing a statistical sample.
Learning outcomes
At the end of the course, the student will have learnt to distinguish statistical and classical definition of probability and will know the formulas that allow us compute the probability of various phenomena. The students will also learn basic ways of treating random variable and the basic methods of describing a statistical sample.
Syllabus
  • Syllabus 1. Random variable. Classical and statistical definition of probability. 2. Theorems about adding and multiplying probabilities. Summation of probabilities. 3. Conditional probability. Independent events. Bayes's theorem. 4. Geometric probability. 5. Statistical definition of probability. Absolute and relative frequency. 6. Random variable. Discrete and continuous random variables and their distribution. Probability function, probability density, distribution function. 7. Basics of descriptive statistics. Arithmetic, geometric, and harmonic mean of a sample, standard deviation, variance. 8. Characteristics of random variables for various kinds of signs (nominal, alternative, interval) 9. Some discrete distributions and their parameters. 10. Some continuous distributions and their parameters 11. Point and interval estimates. 12. Testing hypotheses.
Literature
    recommended literature
  • BUDÍKOVÁ, Marie, Pavel OSECKÝ and Štěpán MIKOLÁŠ. Popisná statistika (Descriptive statistics). 4. vydání. Brno: MU Brno, 2007, 52 pp. ISBN 978-80-210-4246-9. 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
  • OSECKÝ, Pavel. Statistické vzorce a věty (Statistical formulas). Druhé rozšířené. Brno (Czech Republic): Masarykova univerzita, Ekonomicko-správní fakulta, 1999, 53 pp. ISBN 80-210-2057-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika. Sbírka příkladů. (Probability Theory and Mathematical Statistics. Collection of Tasks.). 2.,přepracované vyd. Brno: Masarykova univerzita Brno, 1998, 127 pp. ISBN 80-210-1832-1. info
Teaching methods
Theoretical lecture, solving problems, homework (solving assigned tasks)
Assessment methods
Written assignment, written and oral exam
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2025, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2025/MA0008