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Mathematical Statistics - NMST701

Title:	Matematická statistika
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015
Semester:	summer
E-Credits:	2
Hours per week, examination:	summer s.:2/0, 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:	RNDr. Jitka Zichová, Dr.
Classification:	Mathematics > External Subjects, Probability and Statistics

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Annotation -

Last update: G_M (07.05.2014)

An introductory course of mathematical statistics for students of chemistry at Charles University.

Aim of the course -

Last update: G_M (07.05.2014)

Learn basic principles of probability theory and mathematical

statistics.

Course completion requirements - Czech

Last update: RNDr. Jitka Zichová, Dr. (20.04.2018)

Složení písemné zkoušky.

Literature - Czech

Last update: RNDr. Jitka Zichová, Dr. (27.01.2016)

Jiří Anděl: Statistické metody. Matfyzpress, Praha, 2007.

Jiří Anděl: Matematika náhody. Matfyzpress, Praha, 2000.

Karel Zvára, Josef Štěpán: Pravděpodobnost a matematická statistika.

Matfyzpress, Praha, 2002.

Karel Zvára: Biostatistika. Karolinum, Praha, 2008.

Karel Zvára: Základy statistiky v prostředí R. Karolinum, Praha, 2013.

Teaching methods -

Last update: G_M (07.05.2014)

Lecture.

Requirements to the exam - Czech

Last update: RNDr. Jitka Zichová, Dr. (03.06.2022)

Zkouška je písemná v trvání 1 hodina. Studenti řeší sadu úloh s náplní danou sylabem předmětu. Požaduje se znalost definic základních pojmů, odvození jednoduchých vzorců, schopnost aplikovat teorii na řešení praktických příkladů, pochopení základních myšlenek pokročilejší statistiky (testování hypotéz, intervalové odhady, lineární regrese). Jedinou povolenou pomůckou je kalkulačka. Podrobné požadavky ke zkoušce lze nalézt na webové stránce vyučující.

Syllabus -

Last update: T_KPMS (02.06.2016)

1) Introduction.

2) Descriptive statistics.

3) Basics of probability theory (random events, the definition of probability, conditional probability, independent events).

4) Random variable and its distribution. Characteristics of random variable. Examples of probability distributions.

5) Random vectors. Independent random variables, correlation.

6) Random sample. The law of large numbers. The central limit theorem.

7) Probabilistic and statistical approach in exploring real world. Estimates of the random variable characteristics.

8) Estimation theory. Hypothesis testing. Mathematical statistics as a basic tool for drawing conclusions from a scientific experimental work.

9) Selected statistical tests (one sample test, two sample test, paired test, some nonparametric tests, independence testing in contingency table.).

10) Linear regression model.