Course detail
Statistics and Probability
FSI-CS1-KAcad. year: 2024/2025
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
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).
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Montgomery, D. C. - Renger, G.: Probability and Statistics. New York : John Wiley & Sons, 2017.
Sprinthall, R. C.: Basic Statistical Analysis. Boston : Allyn and Bacon, 1997.
Recommended reading
Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
Seger, J. - Hindls, R.: Statistické metody v tržním hospodářství. Praha : Victoria Publishing, 1995.
Elearning
Classification of course in study plans
Type of course unit
Guided consultation in combined form of studies
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
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.
Elearning