Course details

# Probability and Statistics

IPT Acad. year 2020/2021 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. Correlation and regression analyses.

Guarantor

Fusek Michal, Ing., Ph.D. (DMAT FEEC BUT)

Deputy Guarantor

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

26 hrs lectures, 26 hrs pc labs

Assessment points

70 exam, 30 exercises

Department

Department of Mathematics (DMAT FEEC BUT)

Lecturer

Instructor

Subject specific learning outcomes and competences

Acquired knowledge can be applied, for example, in other courses or in the BSc/MSc thesis.

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.

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.

Prerequisites

Prerequisite kwnowledge and skills

Secondary school mathematics and selected topics from previous mathematical courses.

Study literature

• Anděl, J.: Statistické metody. Praha: Matfyzpress, 1993. (CS)
• Anděl, J.: Základy matematické statistiky. Praha: Matfyzpress, 2005. (CS)
• Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2016 (CS)
• Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
• Likeš, J., Machek, J.: Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1988. (CS)
• Likeš, J., Machek, J.: Počet pravděpodobnosti. Praha: SNTL - Nakladatelství technické literatury, 1987. (CS)
• Neubauer, J., Sedlačík, M., Kříž, O.: Základy statistiky. Praha: Grada Publishing, 2012. (CS)

Fundamental literature

• Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2016 (CS)
• Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
• Anděl, J.: Matematická statistika. Praha: SNTL, 1978. (CS)
• Anděl, J.: Statistické metody. Praha: Matfyzpress, 1993. (CS)
• Anděl, J.: Základy matematické statistiky. Praha: Matfyzpress, 2005. (CS)
• Casella, G., Berger, R. L.: Statistical Inference. Pacific Grove, CA: Duxbury Press, 2001. (EN)
• Hogg, R. V., McKean, J., Craig, A. T.: Introduction to Mathematical Statistics. Boston: Pearson Education, 2013. (EN)
• Likeš, J., Machek, J.: Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1988. (CS)
• Likeš, J., Machek, J.: Počet pravděpodobnosti. Praha: SNTL - Nakladatelství technické literatury, 1987. (CS)
• Montgomery, D. C., Runger, G. C.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2011. (EN)
• Neubauer, J., Sedlačík, M., Kříž, O.: Základy statistiky. Praha: Grada Publishing, 2012. (CS)

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

• Written tests: 30 points.
• Final exam: 70 points.

Controlled instruction

Class attendance. If students are absent due to medical reasons, they should contact their lecturer.

Exam prerequisites

Get at least 10 points during the semester.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Monexerciselectures T8/302 11:0012:50 2BIA 2BIB 3BIT xx Fusek
Monlecturelectures E104 E105 E112 11:0012:50 2BIA 3BIT xx Hlavičková
Monlecturelectures T12/2.173 13:0014:50 2BIB 3BIT xx Fusek
Tueexam2021-02-02 A218 C228 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 T8/010 T8/020 T8/030 12:0013:50 2BIA 2BIB 3BIT 2. oprava
Tueexerciselectures T8/302 15:0016:50 2BIA 2BIB 3BIT xx Fusek
Tueexerciselectures T8/312 15:0016:50 2BIA 2BIB 3BIT xx Hlavičková
Tueexerciselectures T8/302 17:0018:50 2BIA 2BIB 3BIT xx Fusek
Wedexerciselectures A113 12:0013:50 2BIA 2BIB 3BIT xx Hlavičková
Wedexercise2., 3., 4., 6. of lectures A113v 12:0015:50TM, konzultace, Hlavičková
Wedexerciselectures A113 14:0015:50 2BIA 2BIB 3BIT xx Hlavičková
Wedexerciselectures T8/312 15:0016:50 2BIA 2BIB 3BIT xx Fusek
Thuexerciselectures T8/302 07:0008:50 2BIA 2BIB 3BIT xx Fusek
Thuexerciselectures T8/302 09:0010:50 2BIA 2BIB 3BIT xx Fusek
Thuexerciselectures T8/302 11:0012:50 2BIA 2BIB 3BIT xx Fusek
Thuexerciselectures T8/302 15:0016:50 2BIA 2BIB 3BIT xx Hlavičková
Thuexerciselectures T8/302 17:0018:50 2BIA 2BIB 3BIT xx Hlavičková
Friexam2021-01-15 A112 A113 A218 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 T10/1.36 T12/2.173 T12/SF1.141 T8/010 T8/020 T8/030 08:0009:50 2BIA 2BIB 3BIT řádná
Friexam2021-01-15 A112 A113 A218 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 L314 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 10:0011:50 2BIA 2BIB 3BIT řádná
Friexam2021-01-22 A112 A113 A218 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 S206 T10/1.36 T12/2.173 T12/SF1.141 T8/010 T8/020 T8/030 12:0013:50 2BIA 2BIB 3BIT 1. oprava
Friexam2021-01-22 A218 C228 D0206 D0207 D105 E112 G108 G202 M103 M104 M105 N103 N104 N105 N203 N204 N205 O204 S206 17:0018:50 2BIA 2BIB 3BIT 1. oprava

Course inclusion in study plans

• Programme BIT, 2nd year of study, Compulsory
• Programme IT-BC-3, field BIT, 2nd year of study, Compulsory