## Mathematics III

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Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * Level of Course Unit * Year of Study * 230-0203/01 5 ECTS credits Compulsory First Cycle Second Year Winter Semester Face-to-face Czech, English Course succeeds to compulsory courses of previous semester PAL39 RNDr. Radomír Paláček, Ph.D. 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. 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. 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. 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/ 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. Lectures, Individual consultations, Tutorials, Other activities Credit and Examination Credit and Examination 100 (100) 51 Credit Credit 20 5 Examination Examination 80 (80) 30 Písemná zkouška Written examination 60 25 Ústní zkouška Oral examination 20 5