Course detail
Probability and Statistics
FIT-IPTAcad. year: 2020/2021
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.
Supervisor
Department
Learning outcomes of the course unit
Acquired knowledge can be applied, for example, in other courses or in the BSc/MSc thesis.
Prerequisites
Secondary school mathematics and selected topics from previous mathematical courses.
- recommended prerequisite
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
Recommended or required reading
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)
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
- Written tests: 30 points.
- Final exam: 70 points.
Exam prerequisites:
Get at least 10 points during the semester.
Language of instruction
Czech, English
Work placements
Not applicable.
Aims
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.
Specification of controlled education, way of implementation and compensation for absences
Class attendance. If students are absent due to medical reasons, they should contact their lecturer.
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
- 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.
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
eLearning
eLearning: currently opened course