Course detail

Probability and Statistics I

FSI-S1PAcad. year: 2025/2026

The course makes students familiar with descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameter estimation, tests of hypotheses and statistical software Statistica. Seminars include solving problems and applications related to mechanical engineering.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Rudiments of the differential and integral calculus.

Rules for evaluation and completion of the course

Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing both written exams and semester assignment acceptance.
Examination: Evaluation based on points obtained for semester assignment (0-10 points) and a test (0-90points). The exam test consists of two parts: a practical part (2 tasks from the theory of probability: probability and its properties, random variable, distribution Bi, H, Po, N and discrete random vector; 2 tasks from mathematical statistics: point and interval estimates of parameters, tests of hypotheses of distribution and parameters); a theoretical part (4 tasks related to basic notions, their properties, sense and practical use,and proofs of two theorems); evaluation: each task 0 to 15 points and each theoretical question 0 to 5 points; evaluation according to the total number of points (scoring 0 points for semestral assignment, any practical part task, any theoretical part task means failing the exam): excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).
Participation in the exercise is mandatory and the teacher decides on the compensation for absences.

Aims

The course objective is to make students majoring in Mathematical Engineering acquainted with methods of probability theory, descriptive and mathematical statistics, and with statistical software Statistica as well as to encourage students` stochastic way of thinking for developing mathematical models with the emphasis on engineering branches.
Students obtain needed knowledge from the probability theory, descriptive statistics and mathematical statistics, which will enable them to understand and apply stochastic models of technical phenomena and processes based upon these methods.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Hogg R.V., McKean J., Craig, A.T.: Introduction to Mathematical Statistics. Pearson, Cloth. 2013. (EN)
Michálek, J. Matematická statistika pro informatiky. Praha: Státní pedagogické nakladatelství, 1987. (CS)
Montgomery, D. C. - Runger, G.: Applied Statistics and Probability for Engineers, John Wiley & Sons, New York. 1994. (EN)
Zvára, K., Štěpán, J.: Pravděpodobnost a matematická statistika. Praha : Matfyzpress, 2002. (CS)

Recommended reading

Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
Lamoš, F. - Potocký, R.: Pravdepodobnosť a matematická štatistika. Bratislava : Alfa, 1989.
Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : PLUS, 1994.
Neubauer J., Sedlačík M., Kříž O.: Základy statistiky. Praha: Grada Publishing. 2012. (CS)

Classification of course in study plans

  • Programme B-MAI-P Bachelor's 2 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

Random events, field of events, and probability (properties).
Conditioned probability and independent events(properties).
Reliability of systems. Random variable (types, distribution function).
Functional characteristics of discrete and continuous random variables.
Numerical characteristics of discrete and continuous random variables.
Basic discrete distributions A, Bi, H, Po (properties and use).
Basic continuous distributions R, N, E (properties and use).
Random vector, types, functional and numerical characteristics.
Distribution of transformed random variables.
Random sample, sample characteristics (properties, sample from N).
Parameter estimation (point and interval estimates of parameters Bi and N).
Testing statistical hypotheses.
Testing hypotheses of parameters of Bi and N.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

Descriptive statistics (one-dimensional sample with a quantitative variable). Software Statistica.
Descriptive statistics (two-dimensional sample with a quantitative variables). Combinatorics.
Probability (properties and calculating). Semester work assignment.
Conditioned probability. Independent events.
Written exam (3-4 examples). Functional and numerical characteristics of random variable.
Functional and numerical characteristics of random variable - achievement.
Probability distributions (Bi, H, Po, N), approximation.
Random vector, functional and numerical characteristics.
Point and interval estimates of parameters Bi and N.
Written exam (3-4 examples).
Testing hypotheses of parameters Bi and N.
Testing hypotheses of parameters Bi and N - achievement.
Tests of fit.