Statistics and Probability (FSI-CS1-K)

Academic year 2023/2024
Supervisor: Ing. Josef Bednář, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
Acquaint of students with basic notions, methods and progresses of probability theory, descriptive statistics and mathematical statistics. Formalization of stochastic way thinking for modeling of real phenomenon and processes in an engineering enclosures.
Learning outcomes and competences:
Students obtain needed knowledge from the probability theory, descriptive statistics and mathematical statistics, which them will enable understand and apply stochastic models of technical phenomenon and suits, based upon these methods.
Prerequisites:
Rudiments of the differential and integral calculus.
Course contents:
The subject is aimed at introduce of students to descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameters estimation, tests of hypotheses, and linear regression analysis. The practices include problems and applications in mechanical engineering. A part of exercises will solving by means of statistical software.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:

Seminar credit conditions: active attendance in practices, encompassment of complete subject, classification sufficient or better of written exam and admission of semester assignment. Examination (written form): practical part (2 examples from theory of probability: probability and its properties, random variable, distribution Bi, H, Po, N and discrete random vector; 2 examples from mathematical statistics: point and interval estimates of parameters, tests of hypotheses of distribution and parameters, linear regression model) with own summary of formula; theoretical part (4 questions to basic notions, their properties, sense and practical use); evaluation: each example 0 as far as 20 points and every theoretical question 0 as far as 5 points; classification according to of the total sum of points: 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).
Controlled participation in lessons:
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Type of course unit:
    Guided consultation in combined form of studies  1 × 17 hrs. compulsory                  
    Guided consultation  1 × 35 hrs. optionally                  
Course curriculum:
    Guided consultation in combined form of studies 1. Random events and their probability.
2. Conditioned probability, independent events.
3. Random variable, types, functional characteristics.
4. Numerical characteristics of random variables.
5. Basic discrete distributions Bi, H, Po (properties and use).
6. Basic continuous distributions R, N (properties and use).
7. Two-dimensional discrete random vector, types, functional and numerical characteristics.
8. Random sample, sample characteristics (properties, sample from N).
9. Parameters estimation (point and interval estimates of parameters N and Bi).
10. Testing statistical hypotheses (types, basic notions, test).
11. Testing hypotheses of parameters of N, Bi, and tests of fit.
12. Elements of regression analysis.
13. Linear model, estimations and testing hypotheses.
    Guided consultation 1. Introduction to Statistical Software
2. Descriptive statistics
3. Probability
4. Random variable
5. Random vector
6. Probability distributions (Bi, H, Po, N).
7. Point and interval estimates of parameters N and Bi.
8. Testing hypotheses of parameters N and Bi. Tests of fit.
9. Linear regression (straight line), estimates, tests and plot.
Literature - fundamental:
1. Sprinthall, R. C.: Basic Statistical Analysis. Boston : Allyn and Bacon, 1997.
2. Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, 2017.
3. Anděl, J.: Statistické metody. Praha : Matfyzpress, 1993.
Literature - recommended:
1. Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
2. Cyhelský, L. - Kahounová, J. - Hindls, R.: Elementární statistická analýza. Praha : Management Press, 1996.
3. Seger, J. - Hindls, R.: Statistické metody v tržním hospodářství. Praha : Victoria Publishing, 1995.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-STR-K combined study AIŘ Applied Computer Science and Control -- Cr,Ex 5 Compulsory 1 2 W
B-STR-K combined study SSZ Machine and Equipment Construction -- Cr,Ex 5 Compulsory 1 2 W
B-STR-K combined study STG Manufacturing Technology -- Cr,Ex 5 Compulsory 1 2 W