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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.
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

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: G_M (16.05.2012)

Foundations of probability theory with the emphasis on proof techniques. Recommended for bachelor's program in General Mathematics, specialization Stochastics.

Aim of the course -

Last update: G_M (27.04.2012)

To explain basics of modern probability theory.

Course completion requirements -

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

Written and oral exam.

Literature - Czech

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

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

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

Teaching methods -

Last update: prof. RNDr. Viktor Beneš, DrSc. (14.10.2021)

Presential lecture and exercises. Exercise supported by MOODLE.

Requirements to the exam -

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

Written exam - 3 problems to solve.

Oral exam - according to sylabus.

Syllabus -

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

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.