SubjectsSubjects(version: 861)
Course, academic year 2019/2020
Probability and Statistics - NMAI059
Title: Pravděpodobnost a statistika
Guaranteed by: Department of Software Engineering (32-KSI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 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: taught
Language: Czech, English
Teaching methods: full-time
Additional information:
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
doc. RNDr. Daniel Hlubinka, Ph.D.
Class: Informatika Bc.
Informatika Mgr. - Matematická lingvistika
M Bc. MMIB > Povinné
M Bc. MMIB > 2. ročník
M Bc. MMIT > Povinné
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)
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.

Course completion requirements -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (07.10.2019)

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

Conditions for the credits:

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

2. Written test: At least 50 % of points.

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

2. There will be two retries for the written test during the first two weeks of the exam period or earlier.

Literature -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (29.10.2019)

Mitzenmacher M. and Upfal E., Probability and Computing, Cambridge 2005.

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

Grimmett, G.R. and Stirzaker, D.R., Probability and Random Processes, Oxford Science Publications, 2001

Teaching methods -
Last update: G_M (29.05.2008)


Requirements to the exam -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (11.10.2017)

The exam consists of two-parts written test. The computational part is closely related to the problems stated in the exercise classes. The theoretical part is based on the syllabus of the course modified according to the lectures in given semester. The final mark is then based on the results of both parts of the test.

In very rare situations the written test may be completed by oral part if a decision about the mark is needed.

Both parts of the test must be repeated if any part of the written test is failed.

Syllabus -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

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, two-sample analysis for the difference of means, pair test, chi-square test of fit

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

Entry requirements -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (10.05.2018)

Knowledge required before enrollment:

combinatorics, basic formulas

calculus (sequences, series, integrals)

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