SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Measure theory and probability - OB2310100
Title in English: Míra a pravděpodobnost
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2012
Semester: winter
E-Credits: 2
Examination process: winter s.:
Hours per week, examination: winter s.:0/2 MC [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: RNDr. František Mošna, Dr.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Pre-requisite : OB2310004
Annotation -
Last update: MOSNAF/PEDF.CUNI.CZ (06.11.2008)
Measure and measurability, probability measure, random events, random variables and their distribution, normal distribution.
Aim of the course -
Last update: MOSNAF/PEDF.CUNI.CZ (06.11.2008)

Primary purpose of the course is to make students acquanted with basic concepts of measure theory and their application in probability calculus. Secondary aim is to show students elements of stochastistic way of thinking.

Literature -
Last update: STEHLIKO/PEDF.CUNI.CZ (27.03.2009)

Štěpán J., Machek J.: Pravděpodobnost a statistika pro učitelské studium [skriptum]. SPN Praha 1985.

Lukeš J., Machek J.: Počet pravděpodobnosti, SNTL Praha 1987

Svěšnikov A. A.: Sbírka úloh z teorie pravděpodobnosti, matematické statistiky a teorie náhodných funkcí. SNTL Praha 1971

Půlpán Z.: Míra a pravděpodobnost, Hradec Králové

Riečan B., Lamoš F., Lenárt C.: Pravdepodobnosť a matematická štatistika, Alfa Bratislava 1984

Neubrunn T., Riečan B.: Miera a integrál, Veda Bratislava 1981

Neubrunn T., Riečan B.: Teória miery, Veda Bratislava 1992

Brousek J., Ryjáček Z.: Sbírka řešených příkladů z počtu pravděpodobnosti, ZČU Plzeň 1995

Halmos P. R.: Measure theory, Springer 1974 (Van Nostrad 1950,...)

Teaching methods -
Last update: MOSNAF/PEDF.CUNI.CZ (06.11.2008)

Seminars.

Syllabus -
Last update: MOSNAF/PEDF.CUNI.CZ (06.04.2009)
  • Introduction of measure (Jordan, Lebersque, Hausdorff), set systems, measurability, measure properties.
  • Independence of random events, conditional probability, complete probability theorem, the Bayes theorem.
  • Random variable and ots distribution of probability, charakteristics, discrete and continuous distributions (alternative, binomial, hypergeometric, geometric, Poisson, uniform, exponential), probability density, distribution function.
  • Random vectors, conjugate and marginal density and distribution function, independence of random variables, covariance, corellation.
  • Operation with random variables, Law of great numbers, central limit theorem (Moivre - Laplace theorem), normal distribution, distribution chí-square, Student and Fischer.

 
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