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Course, academic year 2024/2025
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Probability Theory 1 - NMSA333
Title: Teorie pravděpodobnosti 1
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Viktor Beneš, DrSc.
Teacher(s): prof. RNDr. Viktor Beneš, DrSc.
RNDr. Petr Čoupek, Ph.D.
Mgr. Petr Dostál, Ph.D.
Class: M Bc. OM
M Bc. OM > Povinně volitelné
M Bc. OM > Zaměření STOCH
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMSA202
Is co-requisite for: NMSA334
Is pre-requisite for: NMSA351
Is interchangeable with: NSTP050, NSTP144
In complex pre-requisite: NMSA349
Annotation -
Foundations of probability theory with the emphasis on proof techniques. Recommended for bachelor's program in General Mathematics, specialization Stochastics.
Last update: G_M (16.05.2012)
Aim of the course -

To explain basics of modern probability theory.

Last update: G_M (27.04.2012)
Course completion requirements -

Written and oral exam.

Last update: Zichová Jitka, RNDr., Dr. (02.05.2023)
Literature - Czech

Štěpán J.: Teorie pravděpodobnosti. Matematické základy. Academia, Praha, 1987

Lachout, P.: Teorie pravděpodobnosti. Karolinum, Praha, 2004.

Last update: Beneš Viktor, prof. RNDr., DrSc. (04.10.2012)
Teaching methods -

Presential lecture and exercises. Exercise supported by MOODLE.

Last update: Beneš Viktor, prof. RNDr., DrSc. (14.10.2021)
Requirements to the exam -

Written exam - 3 problems to solve.

Oral exam - according to sylabus.

Last update: Zichová Jitka, RNDr., Dr. (02.05.2023)
Syllabus -

Measurability of systems of random variables, distribution function, independence, expectation, types of convergence of sequences and sums of random variables, conditioning, zero-one laws, law of large numbers, weak convergence, convergence in distribution, characteristic function, central limit theorems.

Last update: Beneš Viktor, prof. RNDr., DrSc. (07.10.2019)
Entry requirements -

Course NMSA202.

Last update: Zichová Jitka, RNDr., Dr. (17.05.2024)
 
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