University of West Bohemia
Study programmes & Course catalogue
for academic year 2024/2025
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Course: Probability and Statistics

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Course title Probability and Statistics
Course code KMT/PAS
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 3
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Hložek Filip, Ing. Mgr.
  • Honzík Lukáš, PhDr. Ph.D.
Course content
1. Basic terms from combinatorics. Elementary and random phenomena. Classical definition of probability and its generalization. Space of elementary phenomena, probability space. 2. Axiomatic introduction of probability space. Basic set, set of random phenomena and probability measure P. Properties of individual parts of the probability space. 3. Operations with random phenomena. Conditional probability. Independence of random phenomena. Bayes theorem. Geometric probability. 4. Probability models (selection with and without return, Maxwell-Boltzman scheme, and others) 5. Introduction of the term random variable. Probability function, distribution function. 6. Parameters of random variables. Mean value of random variables, variance, standard deviation. 7. Introduction and properties of the most important discrete random variables. 8. Introduction and properties of the most important continuous random variables. 9. Independent random variables. Covariance and correlation ratio. Methods of measuring the strength of the relationship between two or more random variables. 10. Random vectors - basic characteristics. Multivariate random variables. Marginal distribution function. 11. Law of large numbers. The concept of convergence on the space of random variables. Chebyshev's inequality. Chebyshev's theorem. Central Limit Theorem.

Learning activities and teaching methods
Lecture with practical applications, Individual study, Practicum
  • Contact hours - 52 hours per semester
  • Undergraduate study programme term essay (20-40) - 20 hours per semester
  • Preparation for an examination (30-60) - 35 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
prerequisite
Knowledge
Knowledge of mathematics at the level of KMA/M1, KMT/LA (basics of differential calculus and linear algebra)
Skills
solve more complex combinatorial problems
use classical probability skills
Competences
N/A
N/A
N/A
N/A
learning outcomes
Knowledge
describe the properties of probability as a measure of random phenomena
understand descriptive parameters for random variables
define the concept of multidimensional random variables
define a random variable and understand its use in applications
understand the dependence of two or more random variables
describe known procedures for limit theorems
Skills
analyzovat dané úlohy a řešit je s pomocí znalostí jednotlivých náhodných veličin
aplikovat teoretické znalosti z teorie pravděpodobnosti na konkrétní aplikační úlohy
nalézt vztahy mezi jednotlivými náhodnými veličinami
aplikovat varianty centrální limitní věty i věty o extremálních rozděleních
apply variants of the central limit theorem
Competences
N/A
teaching methods
Knowledge
Practicum
Individual study
Interactive lecture
Přednáška s diskusí
Skills
Seminární výuka
Practicum
Individual study
Interactive lecture
Competences
self-study of students using texts on the portal and selected chapters from foreign literature
Skills demonstration
assessment methods
Knowledge
Combined exam
Test
Seminar work
Written and oral exam Demonstration of solved tasks at the blackboard, analysis of possible errors
Skills
Combined exam
Test
Seminar work
Written and oral exam The student solves theoretical and practical tasks
Competences
The student solves a set of problems, which he demonstrates in front of other classmates. He proceeds to the oral exam if he actively participates in the exercises and has successfully solved the given examples
Recommended literature
  • Anděl, Jiří. Matematika náhody. Vyd. 2. Praha : Matfyzpress, 2003. ISBN 80-86732-07-X.
  • C. M. Grinstead, J. L. Snell. Introduction to Probability. Boston, 1997. ISBN 0821807498.
  • Dupač, Václav; Hušková, Marie. Pravděpodobnost a matematická statistika. Praha : Karolinum, 2001. ISBN 80-246-0009-9.
  • E. T. Jaynes. Probability Theory: The Logic of Science. Cambridge, 2002. ISBN 0521592712.
  • Kahounová, Jana. Praktikum k výuce matematické statistiky I : odhady. Praha : Vysoká škola ekonomická, 2000. ISBN 80-245-0070-1.
  • Meloun, Milan; Militký, Jiří. Statistické zpracování experimentálních dat : v chemometrii, biometrii, ekonometrii a v dalších oborech přírodních, technických a společenských věd. 2. vyd. Praha : East Publishing, 1998. ISBN 80-7219-003-2.
  • Plocki, A.; Tlustý, P. Pravděpodobnost a statistika pro začátečníky a mírně pokročilé. Praha, Prometheus, 2007. ISBN 9788071963301.
  • Prasanna Sahoo. Probability and Mathematical Statistics. University of Louisville, 2013.
  • Prášková Z., Lachout P. Základy náhodných procesů. Karolinum Praha, 1998.
  • Riečan, Beloslav. Pravdepodobnosť a matematická štatistika. 1. vyd. Bratislava : Alfa, 1984.
  • Štěpán, Josef. Teorie pravděpodobnosti : Matematické základy : Vysokošk. učebnice pro stud. matematicko-fyz. fakult. Praha : Academia, 1987.
  • ZVÁRA, K., ŠTĚPÁN, J. Pravděpodobnost a matematická statistika. Vyd. 3. Praha : Matfyzpress, 2002. ISBN 80-85863-93-6.


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University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025