Course detail

# Probability and Statistics

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.

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.

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.

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

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 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 hours, compulsory

Teacher / Lecturer

eLearning