Course detail
Probability and Mathematical Statistics
ÚSI-DSA02Acad. year: 2024/2025
The course is intended for doctoral students and is focused on stochastic modelling and modern methods of statistical analysis (probability, random variables and vectors, random selection and its realization, fitting of probability distributions and estimates of their parameters, testing, of statistical hypotheses, regression analysis) for processing statistical files obtained in the implementation and evaluation of experiments in the framework of students' research work.
Language of instruction
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Aims
Students will acquire deeper knowledge of stochastic modelling and modern methods of mathematical statistics, which will enable them to apply adequate stochastic models of observed phenomena and processes by means of PC calculations.
Study aids
Prerequisites and corequisites
Basic literature
DOWDY, S., WEARDEN, S., CHILKO, D. Statistics for Research. New York: John Wiley & Sons, Inc., 2011. (CS)
KOUTKOVÁ,H., MOLL,I.: Úvod do pravděpodobnosti a matematické statistiky, CERM Brno, 2001
MONTGOMERY, D. C., RUNGER, G. Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, Inc., 2011. (CS)
Recommended reading
KARPÍŠEK, Z. Matematika IV. Pravděpodobnost a matematická statistika. Brno: CERM, 2014. (CS)
KOŽÍŠEK, J., STIEBEROVÁ, B. Statistika v příkladech. Praktické aplikace řešené v MS Excel. Praha: Verlag Dashofer, 2012. (CS)
WALPOLE, R.E., MYERS, R.H.: Probability and Statistics for Engineers and Scientists, MACMILLIAN PUBLISHING COMPANY, New York, 1999
Classification of course in study plans
- Programme DSoIK Doctoral
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory - Programme DSoIP Doctoral
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory
branch SOI , 1 year of study, summer semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Probability distribution for applications.
3. Exploratory analysis for processing statistical files.
4. Random selection - model and properties.
5. Fitting the probability distribution.
6. Estimation of probability distribution parameters.
7. Testing statistical hypotheses about parameters and distributions.
8. Nonparametric tests.
9. Basics of linear regression analysis.
10. Introduction to analysis of variance.
11. Introduction to categorical analysis.
12. Statistical software - features and applications.