SubjectsSubjects(version: 804)
Course, academic year 2017/2018
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Probability and Statistics - NMAI059
Czech title: Pravděpodobnost a statistika
Guaranteed by: Department of Software Engineering (32-KSI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
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: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Daniel Hlubinka, Ph.D.
Class: Informatika Bc.
Informatika Mgr. - Matematická lingvistika
M Bc. MMIB > Povinné
M Bc. MMIB > 2. ročník
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: T_KSI (15.04.2003)

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: G_M (05.06.2008)

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: T_KSI (15.04.2003)

Anděl J., Statistické metody, MATFYZPRESS, Praha 1998.

Bartoszynski R. and Niewiadomska-Budaj M., Probability and Statistical Inference, J. Wiley, 1996.

Jarušková D., Matematická statistika, skriptum ČVUT, Praha 2000.

Zvára K. a Štěpán J., Pravděpodobnost a matematická statistika, MATFYZPRESS, Praha 1997.

Teaching methods -
Last update: G_M (29.05.2008)


Syllabus -
Last update: T_KSI (15.04.2003)

Basic notions of the probability theory - random events, probability, conditional probability, total probability formula and Bayes theorem, independence of random events

Random Variables and their distribution - random variable, discrete random variable, continuous random variables, central limit theorem

Random vectors and their distribution - random vector, characteristics of random vector, independence of random vectors, multidimensional normal distribution

An introduction to mathematical statistics - random sample, ordered sample, review of commonly used descriptive statistics Theory of estimation - point estimators, point estimators of parameters of selected distributions, confidence intervals

Theory of testing of hypotheses - an introduction to the hypotheses testing, One-sample and two-sample analysis for normal distribution, pair test, tests about the coefficient of correlation, chi-square test of fit

Regression - linear regression with one explanatory variable, linear regression with several explanatory variables

Simulations - random number generators and basics of the Monte Carlo simulations

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