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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:	http://www.karlin.mff.cuni.cz/~hlubinka/vyuka.php

Guarantor:	doc. RNDr. Daniel Hlubinka, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIB > 2. ročník M Bc. MMIT M Bc. MMIT > Povinné M Bc. MMIT > 2. ročník
Classification:	Mathematics > Probability and Statistics
Co-requisite :	{One 1st year Analysis course}

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)

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.

Aim of the course -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)

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.

Course completion requirements -

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

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.

Literature - Czech

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

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

2001.

Zápisky k přednášce dostupné na v MOodle UK https://dl1.cuni.cz/course/view.php?id=10744

Teaching methods -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (28.05.2019)

Lecture+exercises.

Requirements to the exam -

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

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

Syllabus -

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

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.

Entry requirements -

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

Knowledge required before enrollment:

combinatorics, basic formulas

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