ID: 0354
Course type: theoretical and methodological
Course coordinator: Aranđelović D. Ivan
Lecturers: Aranđelović D. Ivan, Đukić Lj. Dušan, Jandrlić R. Davorka, Lazović M. Goran, Mutavdžić-Đukić M. Rada, Pejčev V. Aleksandar, Tomanović D. Jelena
Contact: Aranđelović D. Ivan
Level of studies: M.Sc. (graduate) Academic Studies – Mechanical Engineering
ECTS: 6
Final exam type: written+oral
Department: Department of Mathematics
Introduction to applicatios of probability theory, reliability theory, mathematical statistics and their most important application in technics. Introduction to methods of regression analysis and stochastic modelling.
Upon successful completion of this course, students should be able to: 1) Calculate probability and conditional probability of random events. 2) Determine rules of distributions, characteristic functions, expected value and variance of discrete random variables. 3) Determine distribution functions, density functions, characteristic functions, expected value and variance of continuous random variables. 4) Apply learned technique for solving basic problems of Theory of confidentiality and Mathematical statistics. 5) Determine degree and direction of correlation of one dimensional random variables, applying least squares method. 6) Apply learned technique of probability calculation for modeling work of the technical system by Monte Carlo method.
Basic concepts of probability theory. Random events. Conditional probability of an event. Total probability formula. Bayes formula. Bernoulli's Formula and its approximations. Random variables. Central limit theorem. Regression. Mathematical statistics mission. Generally about estimation of distribution parameters. Estimating expected value and variance of a random variable. Methods for estimating distribution parameters. Confidence intervals. Statistical hypothesis testing. Least squares method. Reliability of technical systems. Nonparametric hypothesis testing. Analysis of variance. Planning of statistical experiment. Random numbers. Monte-Carlo method. Random variables modelling. Technical systems simulation.
Basic concepts of probability theory. Random events. Conditional probability of an event. Total probability formula. Bayes formula. Bernoulli's Formula and its approximations. Random variables. Central limit theorem. Regression. Mathematical statistics mission. Generally about estimation of distribution parameters. Estimating expected value and variance of a random variable. Methods for estimating distribution parameters. Confidence intervals. Statistical hypothesis testing. Least squares method. Reliability of technical systems. Nonparametric hypothesis testing. Analysis of variance. Planning of statistical experiment. Random numbers. Monte-Carlo method. Random variables modelling. Technical systems simulation.
No prerequisites.
I. Aranđelović, Z. Mitović, V. Stojanović, Probability and Statistics, Zavod za udžbenike, Beograd 2011. I. Aranđelović, Theory of random events, Vedes, Beograd 2005. S. Radojević, V. Simonović, Problems and exercises from Probability and Statistics, Zavod za udžbenike, Beograd 2014. B. Jaćimović, S. Genić, M. Stamenić, I. Aranđelović, A. Petrović, N. Mitrović, U. Milovančević, M. Ivošević, M. Otović, A. Petrović, R. Rajić, N. Tanasić, M. Mihailović, S. Marković, T. Simonović, Methods and examples of experiential exercises in process engineering and thermotechnics, Beograd 2022.
Total assigned hours: 75
New material: 20
Elaboration and examples (recapitulation): 10
Auditory exercises: 10
Laboratory exercises: 0
Calculation tasks: 15
Seminar paper: 0
Project: 5
Consultations: 0
Discussion/workshop: 0
Research study work: 0
Review and grading of calculation tasks: 5
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 5
Test: 5
Test: 0
Final exam: 0
Activity during lectures: 5
Test/test: 50
Laboratory practice: 0
Calculation tasks: 10
Seminar paper: 0
Project: 5
Final exam: 30
Requirement for taking the exam (required number of points): 20
V. Simonović: Introduction to theory of probability and mathematical statistics, Naučna knjiga, Beograd, 1995. ; Z. A. Ivković: Theory of probability and mathematical statistics, Građevinska knjiga, Beograd, 1980.; S. Vukadinović: Elements of theory of probability and statistics, Beograd 1986.; B. Vidaković, D. Banjević, Probability and statistics, exercises , Beograd 1989. ; M. Nenadović, Mathematical analysis of measurment dates, Beograd 1988.