Course details
Probability and Statistics
IPT Acad. year 2023/2024 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
Course coordinator
Language of instruction
Completion
Time span
- 26 hrs lectures
- 26 hrs exercises
Assessment points
- 80 pts final exam
- 20 pts numeric exercises
Department
Lecturer
Instructor
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.
Why is the course taught
The world around us is complex and we try to describe it using mathematical models. However, not all the models are deterministic. In many situations, randomness plays an important role and some phenomena occur only with a certain probability. Students will learn about the probability, learn how to model the behaviour of random variables and analyze obtained (measured) data using selected methods of mathematical statistics. Overall, probability and related topics are important parts of computer science.
Recommended prerequisites
- Discrete Mathematics (IDM)
- Mathematical Analysis 1 (IMA1)
- Mathematical Analysis 2 (IMA2)
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
- Introduction to probability theory. Combinatorics and classical probability.
- Axiomatic probability. Conditional probability and independence. Probability rules. Total probability, Bayes' theorem.
- Random variable (discrete and continuous), probability mass function, cumulative distribution function, probability density function. Characteristics of random variables (mean, variance, skewness, kurtosis).
- Discrete probability distributions: Bernoulli, binomial, hypergeometric, geometric, Poisson.
- Continuous probability distributions: uniform, exponencial, normal. Central limit theorem.
- Basic arithmetics with random variables and their influence on the parameters of probability distributions.
- 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.
- Introduction to statistics. Descriptive statistics. Data processing. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
- Estimation theory. Point estimates. Maximum likelihood method. Bayesian inference.
- Interval estimates. Statistical hypothesis testing. One-sample and two-sample tests (t-test, F-test).
- Goodness-of-fit tests.
- Introduction to regression analysis. Linear regression.
- Correlation analysies. Pearson's and Spearman's correlation coefficient.
Syllabus of numerical exercises
Practising of selected topics of lectures.
Progress assessment
- Homeworks: 20 points.
- Final exam: 80 points.
Class attendance. If students are absent due to medical reasons, they should contact their lecturer.
Exam prerequisites
Get at least 8 points during the semester.
Schedule
Day | Type | Weeks | Room | Start | End | Capacity | Lect.grp | Groups | Info |
---|---|---|---|---|---|---|---|---|---|
Mon | exercise | lectures | T8/T 3.12 | 07:00 | 08:50 | 56 | 2BIA 2BIB 3BIT | xx | Fusek |
Mon | lecture | lectures | Aula profesora Braunera | 09:00 | 10:50 | 338 | 2BIB 3BIT | 20 - 29 xx | Fusek |
Mon | exam | 2024-01-22 | Aula profesora Braunera | 10:30 | 12:30 | 2. termin - Aula Braunera (Technická 12) | |||
Mon | exam | 2024-01-22 | Aula profesora Kalendovského | 10:30 | 12:30 | 2. termin - Aula Kalendovskeho (Technická 10) | |||
Mon | exam | 2024-01-22 | T8/T 0.10 | 10:30 | 12:30 | 2. termin - T010 (Technická 8) | |||
Mon | exam | 2024-01-22 | T8/T 0.30 | 10:30 | 12:30 | 2. termin - T030 (Technická 8) | |||
Mon | lecture | lectures | E104 E105 E112 | 12:00 | 13:50 | 294 | 2BIA 3BIT | 10 - 19 xx | Hlavičková |
Mon | exercise | lectures | T8/T 3.12 | 15:00 | 16:50 | 56 | 2BIA 2BIB 3BIT | xx | Hlavičková |
Tue | exercise | lectures | T8/T 3.02 | 11:00 | 12:50 | 56 | 2BIA 2BIB 3BIT | xx | Fusek |
Tue | exercise | lectures | T8/T 3.02 | 13:00 | 14:50 | 56 | 2BIA 2BIB 3BIT | xx | Fusek |
Wed | exercise ^{*)} | lectures | A113 | 09:00 | 10:50 | 64 | 2BIA 2BIB 3BIT | xx | Fusek |
Wed | exercise | lectures | A113 | 11:00 | 12:50 | 64 | 2BIA 2BIB 3BIT | xx | Hlavičková |
Wed | exercise | lectures | A113 | 13:00 | 14:50 | 64 | 2BIA 2BIB 3BIT | xx | Hlavičková |
Thu | exercise | 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures | D0207 | 08:00 | 09:50 | 64 | 2BIA 2BIB 3BIT | xx | Fusek |
Thu | exercise | 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures | D0207 | 10:00 | 11:50 | 64 | 2BIA 2BIB 3BIT | xx | Fusek |
Thu | exam | 2024-01-11 | Aula profesora Braunera | 10:30 | 12:30 | 1. termin - Aula Braunera | |||
Thu | exam | 2024-01-11 | Aula profesora Kalendovského | 10:30 | 12:30 | 1. termin - Aula Kalendovskeho | |||
Thu | exam | 2024-01-11 | T12/SF 1.141 | 10:30 | 12:30 | 1. termin - SF1.141 | |||
Thu | exam | 2024-01-11 | T12/SF 2.162 | 10:30 | 12:30 | 1. termin - SF2.162 | |||
Thu | exam | 2024-01-11 | T8/T 0.10 | 10:30 | 12:30 | 1. termin - T010 | |||
Thu | exam | 2024-01-11 | T8/T 0.20 | 10:30 | 12:30 | 1. termin - T020 | |||
Thu | exercise | 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures | T8/T 3.02 | 11:00 | 12:50 | 56 | 2BIA 2BIB 3BIT | xx | Hlavičková |
Thu | exercise | 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures | A113 | 12:00 | 13:50 | 64 | 2BIA 2BIB 3BIT | xx | Fusek |
Thu | exercise ^{*)} | 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures | T8/T 3.02 | 15:00 | 16:50 | 0 | 2BIA 2BIB 3BIT | xx | Hlavičková |
Fri | exercise ^{*)} | 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures | D0207 | 08:00 | 09:50 | 0 | 2BIA 2BIB 3BIT | xx | Fusek |
Fri | exam | 2023-12-15 | Aula profesora Braunera | 09:00 | 11:00 | Predtermin Aula Braunera | |||
Fri | exam | 2023-12-15 | Aula profesora Kalendovského | 09:00 | 11:00 | Predtermin Aula Kalendovskeho | |||
Fri | exercise ^{*)} | 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures | D0207 | 10:00 | 11:50 | 0 | 2BIA 2BIB 3BIT | xx | Fusek |
Fri | exam | 2024-02-02 | T8/T 0.10 | 10:30 | 12:30 | 3. termin - T010 (Technická 8) | |||
Fri | exam | 2024-02-02 | T8/T 0.20 | 10:30 | 12:30 | 3. termin - T020 (Technická 8) | |||
Fri | exam | 2024-02-02 | T8/T 0.30 | 10:30 | 12:30 | 3. termin - T030 (Technická 8) |
Course inclusion in study plans
- Programme BIT, 2nd year of study, Compulsory
- Programme BIT (in English), 2nd year of study, Compulsory
- Programme IT-BC-3, field BIT, 2nd year of study, Compulsory