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

Czech, English

Completion

Credit+Examination (written)

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

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.
6. Basic arithmetics with random variables and their influence on the parameters of probability distributions.
7. 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.
8. Introduction to statistics. Descriptive statistics. Data processing. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
9. Estimation theory. Point estimates. Maximum likelihood method. Bayesian inference.
10. Interval estimates. Statistical hypothesis testing. One-sample and two-sample tests (t-test,  F-test).
11. Goodness-of-fit tests.
12. Introduction to regression analysis. Linear regression.
13. 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

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise lectures T8/T 3.12 07:0008:5056 2BIA 2BIB 3BIT xx Fusek
Mon lecture lectures Aula profesora Braunera 09:0010:50338 2BIB 3BIT 20 - 29 xx Fusek
Mon exam 2024-01-22 Aula profesora Braunera 10:3012:30 2. termin - Aula Braunera (Technická 12)
Mon exam 2024-01-22 Aula profesora Kalendovského 10:3012:30 2. termin - Aula Kalendovskeho (Technická 10)
Mon exam 2024-01-22 T8/T 0.10 10:3012:30 2. termin - T010 (Technická 8)
Mon exam 2024-01-22 T8/T 0.30 10:3012:30 2. termin - T030 (Technická 8)
Mon lecture lectures E104 E105 E112 12:0013:50294 2BIA 3BIT 10 - 19 xx Hlavičková
Mon exercise lectures T8/T 3.12 15:0016:5056 2BIA 2BIB 3BIT xx Hlavičková
Tue exercise lectures T8/T 3.02 11:0012:5056 2BIA 2BIB 3BIT xx Fusek
Tue exercise lectures T8/T 3.02 13:0014:5056 2BIA 2BIB 3BIT xx Fusek
Wed exercise *) lectures A113 09:0010:5064 2BIA 2BIB 3BIT xx Fusek
Wed exercise lectures A113 11:0012:5064 2BIA 2BIB 3BIT xx Hlavičková
Wed exercise lectures A113 13:0014:5064 2BIA 2BIB 3BIT xx Hlavičková
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures D0207 08:0009:5064 2BIA 2BIB 3BIT xx Fusek
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures D0207 10:0011:5064 2BIA 2BIB 3BIT xx Fusek
Thu exam 2024-01-11 Aula profesora Braunera 10:3012:30 1. termin - Aula Braunera
Thu exam 2024-01-11 Aula profesora Kalendovského 10:3012:30 1. termin - Aula Kalendovskeho
Thu exam 2024-01-11 T12/SF 1.141 10:3012:30 1. termin - SF1.141
Thu exam 2024-01-11 T12/SF 2.162 10:3012:30 1. termin - SF2.162
Thu exam 2024-01-11 T8/T 0.10 10:3012:30 1. termin - T010
Thu exam 2024-01-11 T8/T 0.20 10:3012:30 1. termin - T020
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 11:0012:5056 2BIA 2BIB 3BIT xx Hlavičková
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 12:0013:5064 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 15:0016:500 2BIA 2BIB 3BIT xx Hlavičková
Fri exercise *) 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures D0207 08:0009:500 2BIA 2BIB 3BIT xx Fusek
Fri exam 2023-12-15 Aula profesora Braunera 09:0011:00 Predtermin Aula Braunera
Fri exam 2023-12-15 Aula profesora Kalendovského 09:0011:00 Predtermin Aula Kalendovskeho
Fri exercise *) 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures D0207 10:0011:500 2BIA 2BIB 3BIT xx Fusek
Fri exam 2024-02-02 T8/T 0.10 10:3012:30 3. termin - T010 (Technická 8)
Fri exam 2024-02-02 T8/T 0.20 10:3012:30 3. termin - T020 (Technická 8)
Fri exam 2024-02-02 T8/T 0.30 10:3012:30 3. termin - T030 (Technická 8)
It is not possible to register this class in Studis. (Some exercises may be opened later if needed, but this is not guaranteed.)

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