Course Details

Mathematics 4

Academic Year 2025/26

BAA004 course is part of 9 study plans

​ BPA-SI Winter Semester 3rd year

​ BPC-SI / S Winter Semester 3rd year

​ BPC-SI / K Winter Semester 3rd year

​ BPC-SI / E Winter Semester 3rd year

​ BPC-SI / M Winter Semester 3rd year

​ BPC-SI / V Winter Semester 3rd year

​ BPC-MI Winter Semester 2nd year

​ BPC-EVB Winter Semester 3rd year

​ BKC-SI Winter Semester 3rd year

Course Guarantor

Ing. Jan Holešovský, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

The students should get an overview of the basic properties of probability to be able to deal with simple practical problems dealing with stochastic uncertainty. They should get familiar with the basic statistical methods used for point and interval estimates, testing statistical hypotheses, and linear model. Student will be able to solve simple practical probability problems and to use basic statistical methods, estimates of parameters and parametric functions, testing statistical hypotheses, and linear models.

Language of instruction

Czech, English

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289590

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  1. Random events (basic properties, operations), probability (classical, axiomatic) and its properties.
  2. Conditional probability and the law of total probability, Bayes' theorem, independence of random events.
  3. Random variable: introduction, cumulative distribution function, density function and probability mass function.
  4. Numeric characteristics of random variables: mean, variance, standard deviation, modus, quantiles. Rules of calculation mean and variance.
  5. Discrete probability distributions: Bernoulli, binomial, hypergeometric and Poisson.
  6. Continuous probability distributions: uniform, normal, chi2, Student's and Fisher-Snedecor distribution.
  7. Bivariate discrete random vector, joint and marginal distributions, independence of the components, numeric characteristics.
  8. Random sample and sample statistics (properties, their distribution for sample from N). Central limit theorem.
  9. Point estimates (unbiased, best, consistent) and interval estimates for parameters of normal and Bernoulli random variables.
  10. Testing statistical hypothesis: principle and one-sample tests (z test, t test, chi2 test for variance, asymptotic test for the parameter of Bernoulli distribution).
  11. Two-sample tests: F test, t test for unknown variances under homoscedasticity or heteroscedasticity, paired t test, equality test for parameters of two Bernoulli distributions.
  12. Goodness-of-fit tests: chi2 test, graphical diagnostics (histogram, QQ plot, PP plot), and some alternatives.
  13. Introduction to regression analysis.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  1. Descriptive statitics for univariate data.
  2. Classical probability and its calculation, application of basec properties.
  3. Conditional probability and the law of total probabilty, Bayes' rule and independence of random events.
  4. Functional and numerical characteristis of random variables.
  5. Functional and numerical characteristis of random variables - continuation.
  6. Transformation of random variable. Discrete probability distributions.
  7. Discrete (binomial, hypergeometric, Poisson) and continuous (normal) probability distributions.
  8. Test. Approximation of distributions.
  9. Bivariate discrete random vector: functional and numerical characteristics, independence of its components.
  10. Point and interval estimates for parameters of normal and Bernoulli random variables.
  11. One-sample tests of hypotheses about the parameters of normal and Bernoulli distributions.
  12. Two-sample tests of hypotheses about the parameters of normal and Bernoulli distributions.
  13. Goodness-of-fit tests.