IPT Acad. Classical probability. Axiomatic probability. Conditional probability.

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IPT Acad. 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. 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. Subject specific learning outcomes and competences.

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. The world around us is complex and we try to describe it using mathematical models. However, not all the models are deterministic. 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. Prerequisite kwnowledge and skills. Syllabus of numerical exercises. Class attendance. If students are absent due to medical reasons, they should contact their lecturer. Course inclusion in study plans. Fusek Michal, Ing. Deputy Guarantor. Language of instruction.

Time span. Assessment points. Learning objectives. Why is the course taught. Mathematical Analysis 2 IMA2. Secondary school mathematics and selected topics from previous mathematical courses. Study literature. Praha: Matfyzpress, CS Fajmon, B. CS Neubauer, J. Praha: Grada Publishing, Fundamental literature. Fajmon, B. Praha: SNTL, CS Casella, G. EN Hogg, R.

Boston: Pearson Education, CS Montgomery, D. EN Neubauer, J. Syllabus of lectures. Introduction to probability theory. Combinatorics and classical 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. 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. Data processing. Characteristics of central tendency, variability and shape. Graphical representation of the data. Point estimates. Interval estimates. Linear regression. Pearson's and Spearman's correlation coefficient. Conjugate prior.

Posterior predictive distribution. Practising of selected topics of lectures. Progress assessment. Written tests: 30 points. Final exam: 70 points. Controlled instruction. Exam prerequisites. Get at least 10 points during the semester.

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