Course detail

Statistics and Probability

FSI-CS1 Acad. year: 2027/2028 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

Ing. Ivan Eryganov, Ph.D.

Department

Institute of Mathematics

Entry knowledge

Fundamentals of differential and integral calculus. 

Rules for evaluation and completion of the course

Credit is awarded upon active participation in compulsory classes, successful completion of the test, and acceptance of the semester assignment.

The semester assignment is completed in JMP (or another statistical software) directly during computer-assisted practical classes. It assesses students’ ability to process the assigned data, select appropriate methods, and interpret the results.

The examination is written; students must obtain credit before taking it. The practical part consists of four problems: two in probability theory and two in mathematical statistics. Students may use their own formula sheet during the practical part. Each problem is worth 0–20 points, giving a maximum of 80 points. The theoretical part consists of four questions covering basic concepts, their properties, meaning, and practical applications. Each question is worth 0–5 points, giving a maximum of 20 points.

The probability problems cover event probabilities, random variables, binomial, hypergeometric, Poisson, and normal distributions, and discrete random vectors. The statistics problems cover point and interval estimation, hypothesis tests concerning parameters and distributions, and linear regression.

The final grade is based on the total examination score (a maximum of 100 points). Credit requirements are assessed separately. The grading scale is: A (excellent), 90–100 points; B (very good), 80–89 points; C (good), 70–79 points; D (satisfactory), 60–69 points; E (sufficient), 50–59 points; F (fail), 0–49 points. A minimum of 50 points is required to pass the examination.

Attendance at computer-assisted practical classes is compulsory; attendance at lectures is optional.

The teacher determines how missed compulsory classes are to be made up.

Aims

On successful completion, the student will be able to:

  1. Summarise univariate and bivariate data using descriptive statistics and graphs and interpret the results in an engineering context.
  2. Calculate event probabilities, including conditional probabilities, and assess independence.
  3. Determine distributional and numerical characteristics of random variables and discrete random vectors and select a suitable basic probability distribution.
  4. Construct point estimates and confidence intervals for normal and binomial parameters and explain their meaning.
  5. Formulate and perform statistical tests of parameters or distributions, assess assumptions and interpret conclusions.
  6. Fit and evaluate a simple linear regression model; use JMP to analyse assigned data and interpret the output in context.

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 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

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

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.