Mathematics III

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Course Unit Code230-0203/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
PAL39RNDr. Radomír Paláček, Ph.D.
Summary
Combinatorics and probability. Random events, operations with them, sample space.
Definitions of events' probability - classical, geometrical, statistics. Conditional probability. Total probability
and independent events.
Random variable and its characteristics.
Basic types of probability distributions of discrete random variables.
Basic types of probability distributions of continuous random variables.
Random vector, probability distribution, numerical characteristics.
Statistical file with one factor. Grouped frequency distribution.
Statistical file with two factors.
Regression and correlation.
Random sample, point and interval estimations of parameters.
Hypothesis testing.iables: two-dimensional integrals, three-dimensional integrals,
line integral of the first and the second kind.
Probabilities of random events: axioms of probability,
conditional probability, independence. Random variables: discrete random
variables, continuous random variables, expected values. Important practical
distributions of discrete and continuous random variables.
Learning Outcomes of the Course Unit
The aim of the course is to provide theoretical and practical foundation for understanding of the meaning of basic
probability terms and teach the student to statistical thinking as a way of understanding of the processes and
events around us, to acquaint him with the basic methods of statistical data gathering and analyzing, and to show
how to use these general procedures in other subjects of study and in practice.

Graduates of this course should be able to:
• understand and use the basic terms of combinatorics and probability theory;
• formulate questions that can be answered by the data, learn the principles of data collecting, processing and
presenting;
• select and use appropriate statistical methods for data analysis;
• propose and evaluate conclusions (inferences) and predictions using the data.
Course Contents
Syllabus of lecture

Combinatorics. Random events and their operations.
Probabilities of random events - clasical, geometrical, statistical. Conditional probability. Composite probability.
Bernoulli sequence of independent random trials. Bayes formula.
Discrete and continuous random variable. Probability mass and density function. Probability distribution funciton.
Characteristics of random variables.
Basic types of probability distributions of discrete and continuous random variables.
Random vectors, their probabilities distribution and characteristics.
Processing of the statistical sample.
Random selection, point and interval estimates.
Testing of hypothesis - parametrical and nonparametrical tests.
Linear regression. Least square method.
Recommended or Required Reading
Required Reading:
Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1
Doležalová, J.-Pavelka, L.: Pravděpodobnost a statistika. Skriptum VŠB, Ostrava 2005. ISBN 80-248-0948-6.
Otipka, P.-Šmajstrla, V.: Pravděpodobnost a statistika. Skriptum VŠB-TU, Ostrava 2006. ISBN 80-248-1194-4. ( http://www.studopory.vsb.cz/studijnimaterialy/past/past.pdf )
mdg.vsb.cz/portal/
www.studopory.vsb.cz/
http://homen.vsb.cz/~oti73/cdpast1/
Recommended Reading:
Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1
Hradecký, P. a kol.: Pravděpodobnost. Skriptum VŠB-TU, Ostrava 1998. ISBN 80-7078-442-3.
Hendl, J.: Přehled statistických metod zpracování dat. Praha : Portál, 2004. ISBN 80-7178-820-1.
Cyhelský, L. - Hustopecký, J. - Závodský, P.: Příklady k základům statistiky. Praha: SNTL 1988.
Anděl, J.: Matematická statistika, SNTL/Alfa, Praha 1978.
Mielcová, E. - Stoklasová, R. - Ramík, J.: Statistické programy, e-learningové skriptum, Slezská Univerzita, Opava.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5