Course detail
Statistics and Probability
FSI-CS1 Acad. year: 2024/2025 Winter semester
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
Czech
Number of ECTS credits
5
Supervisor
Department
Entry knowledge
Rudiments of the differential and integral calculus.
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
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.
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.
The study programmes with the given course
Programme B-ENE-P: Energy, Bachelor's, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization AIŘ: Applied Computer Science and Control, compulsory
Programme C-AKR-P: , Lifelong learning
specialization CZS: , elective
Programme B-STR-P: Engineering, Bachelor's
specialization KSB: Quality, Reliability and Safety, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization SSZ: Machine and Equipment Construction, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization STG: Manufacturing Technology, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
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.
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
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.