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Course, academic year 2023/2024
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Probability - NMSA211
Title: Pravděpodobnost
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2, 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
Additional information:
Guarantor: doc. RNDr. Daniel Hlubinka, Ph.D.
Class: M Bc. MMIB
M Bc. MMIB > Povinné
M Bc. MMIB > 2. ročník
M Bc. MMIT > Povinné
M Bc. MMIT > 2. ročník
Classification: Mathematics > Probability and Statistics
Co-requisite : {One 1st year Analysis course}
Annotation -
Basic notions of the probability and statistics will be introduced and examples of applications will be given. It concerns especially of the notion of probability, random variable and of its distribution, independence, random sample and its descriptive characteristics, construction of estimators, testing of hypotheses and random number generation. Emphasis will be especially on the practical use of above mentioned methods using freely available statistical software.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (28.05.2019)
Aim of the course -

The students will learn basics of the probability theory and mathematical statistics. The will be able to understand the core of stochastic procedures presented in other courses.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (28.05.2019)
Course completion requirements -

The credits for exercise classes are necessary condition for the exam.

Conditions for the credits:

1. Attendance in the classes: at most 3 abseneces during the semester.

2. Written test: at least 51% of points.

The nature of the credits excludes a retry. Condition 2. may be once retried.

Last update: Zichová Jitka, RNDr., Dr. (01.05.2020)
Literature - Czech

Karel Zvára, Josef Štěpán: Pravděpodobnost a matematická statistika, Matfyzpress, Praha, 2012.

Ronald Meester. A Natural Introduction to Probability Theory 2nd ed. Birkhäuser 2008

Geoffrey Grimmett , David Stirzaker. Probability and Random Processes. Oxford 2001.

Geoffrey Grimmett , David Stirzaker. One Thousand Exercises in Probability. Oxford


Zápisky k přednášce dostupné na v MOodle UK​

Last update: Hlubinka Daniel, doc. RNDr., Ph.D. (29.09.2020)
Teaching methods -


Last update: Kaplický Petr, doc. Mgr., Ph.D. (28.05.2019)
Requirements to the exam -

The written part of exam consists of numerical exercises. The oral part is focused on theory and its application.

Last update: Zichová Jitka, RNDr., Dr. (01.05.2020)
Syllabus -

Introduction to probability theory and statistical induction.

Axiomatic definition of probability, computation of probability, conditional probability and Bayes formula.

Random variables and vectors and their distribution, characteristics of random variables.

Convergence in probability and in distribution, law of large numbers and central limit theorem, Markov, Čebyšev and Chernoff inequalities.

Applications of limit theorems and inequalities.

Statistical estimation based on limit theorems.

Last update: Zichová Jitka, RNDr., Dr. (01.05.2020)
Entry requirements -

Knowledge required before enrollment:

combinatorics, basic formulas

elementary calculus (sequences, series, integrals), linear algebra.

Last update: Zichová Jitka, RNDr., Dr. (01.05.2020)
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