Course detail

Probability and Statistics

FIT-IPTAcad. year: 2019/2020

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.

Language of instruction

Czech, English

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Ing. Michal Fusek, Ph.D.

Department

Department of Mathematics (UMAT)

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.

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Basic literature

Not applicable.

Recommended reading

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)
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)
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)
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)

Classification of course in study plans

  • Programme BIT Bachelor's 2 year of study, winter semester, compulsory

  • Programme IT-BC-3 Bachelor's

    branch BIT , 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Michal Fusek, Ph.D.

Syllabus

  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. Descriptive statistics. Data processing. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
  9. Random sample. Point estimates. Maximum likelihood method.
  10. Interval estimates. Statistical hypothesis testing. One-sample and two-sample tests (t-test,  F-test).
  11. Goodness-of-fit test. Analysis of variance (ANOVA). One-way and two-way ANOVA.
  12. Correlation and regression analyses. Linear regression. Pearson's and Spearman's correlation coefficient.
  13. Bayesian statistics. Conjugate prior. Maximum a posteriori probability (MAP) estimate. Posterior predictive distribution.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Michal Fusek, Ph.D.