Course details

Probability and Statistics

IPT Acad. year 2026/2027 Winter semester 5 credits

Classical probability. Axiomatic probability. Conditional probability. Total probability. Bayes' theorem. Random variable and random vector.  Characteristics of random variables and vectors. Discrete and continuous probability distributions. Central limit theorem. Transformation of random variables. Independence. Multivariate normal distribution. Descriptive statistics. Random sample. Point and interval estimates. Maximum likelihood method. Statistical hypothesis testing. Goodness-of-fit test. Analysis of variance. Correlation and regression analyses. Bayesian statistics.

Guarantor

Novotná Veronika, doc. Mgr., Ph.D. (ÚKI)

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

  • 26 hrs lectures
  • 26 hrs exercises

Assessment points

  • 80 pts final exam

Department

Department of Quantitative Engineering (ÚKI)

Lecturer

Křápek Milan, Mgr., Ph.D. (ÚKI)

Instructor

Křápek Milan, Mgr., Ph.D. (ÚKI)
Morozov Anton, Ing. Mgr. (ÚKI)

Learning objectives

The main goal of the course is to introduce basic principles and methods of probability and mathematical statistics which are useful not only in computer sciences.
Acquired knowledge can be applied, for example, in other courses or in the BSc/MSc thesis.

Recommended prerequisites

Prerequisite knowledge and skills

Secondary school mathematics and selected topics from previous mathematical courses.

Study literature

  • Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
  • Montgomery, D. C., Runger, G. C.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2011. (EN)

Syllabus of lectures

  1. Introduction to probability theory. Combinatorics and classical probability.
  2. Axiomatic probability. Conditional probability and independence. Probability rules. Total probability, Bayes' theorem.
  3. Random variable (discrete and continuous), probability mass function, cumulative distribution function, probability density function. Characteristics of random variables (mean, variance, skewness, kurtosis).
  4. Discrete probability distributions: Bernoulli, binomial, hypergeometric, geometric, Poisson.
  5. Continuous probability distributions: uniform, exponencial,  normal. Central limit theorem. Basic arithmetics with random variables and their influence on the parameters of probability distributions.
  6. Random vector (discrete and continuous). Joint and marginal probability mass function, cumulative distribution function, probability density function. Characteristics of random vectors (mean, variance, covariance, correlation coefficient). Independence. Multivariate normal distribution.
  7. Introduction to statistics. Descriptive statistics. Data processing.
  8. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
  9. Estimation theory. Point estimates. Maximum likelihood method. Bayesian inference. Interval estimates.
  10. Statistical hypothesis testing. One-sample and two-sample tests (t-test,  F-test).
  11. Goodness-of-fit and normality tests. Test of independence.
  12. Correlation analysies. Pearson's and Spearman's correlation coefficient.
  13. Introduction to regression analysis. Linear regression.

Syllabus of numerical exercises

Practising of selected topics of lectures. 

Progress assessment

  • Active participation in exercises: 20 points.
  • Final exam: 80 points. 
  • Exam prerequisites: get at least 12 points during the semester. 



Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise 1., 2., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures M203 14:0015:5040 2BIA 2BIB 3BIT xx
Mon exercise 1., 2., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures M203 16:0017:5040 2BIA 2BIB 3BIT xx
Tue exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12., 13. of lectures IO/P292 09:0010:5040 2BIA 2BIB 3BIT xx Morozov
Tue exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12., 13. of lectures IO/P292 11:0012:5040 2BIA 2BIB 3BIT xx Morozov
Tue exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12., 13. of lectures IO/P292 13:0014:5040 2BIA 2BIB 3BIT xx Křápek
Tue exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12., 13. of lectures IO/P292 15:0016:5040 2BIA 2BIB 3BIT xx Morozov
Tue lecture 1., 2., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures E104 E105 E112 17:0018:50294 2BIB 3BIT 20 - 29 xx Křápek
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures IO/P292 11:0012:5040 2BIA 2BIB 3BIT xx
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures IO/P292 13:0014:5040 2BIA 2BIB 3BIT xx
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures IO/P292 15:0016:5040 2BIA 2BIB 3BIT xx
Wed exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures IO/P292 17:0018:5040 2BIA 2BIB 3BIT xx
Thu exercise lectures A113 08:0009:5040 2BIA 2BIB 3BIT xx
Thu lecture lectures IO/P384 13:0014:50294 2BIB 3BIT 20 - 29 xx Křápek
Fri exercise lectures M203 08:0009:5040 2BIA 2BIB 3BIT xx Morozov
Fri exercise lectures M203 12:0013:5040 2BIA 2BIB 3BIT xx Morozov
Fri exercise lectures M203 14:0015:5040 2BIA 2BIB 3BIT xx Morozov

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme BIT (in English), 2nd year of study, Compulsory
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