SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Probability - NMSA211
Title in English: Pravděpodobnost
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
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
Classification: Mathematics > Probability and Statistics
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.

Literature - Czech
Last update: doc. Mgr. Petr Kaplický, Ph.D. (29.05.2019)

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

Michael Mitzenmacher, Eli Upfal. Probability and Computing. Cambridge 2005

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

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

Lecture+exercises.

Syllabus - Czech
Last update: doc. Mgr. Petr Kaplický, Ph.D. (29.05.2019)

Základy teorie pravděpodobnosti a statistického uvažování.

Matematická axiomatika pravděpodobnosti, výpočetní vzorce, náhodné veličiny a vektory a jejich

rozdělení, charakteristiky náhodných veličin.

Konvergence v pravděpodobnosti a v distribuci, zákon velkých čísel a centrální limitní věta,

Markovova, Čebyševova a Chernoffova nerovnost.

Použití limitních vět a nerovností.

Odhad parametru a pravděpodobnosti pomocí limitních vět.

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

Knowledge required before enrollment:

combinatorics, basic formulas

calculus (sequences, series, integrals)

 
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