Probability and information theory (5cr)

Objective

You know the basic concepts of probability and information theory. You are able to make decisions by means of random variables and probability distributions. You are able to apply information theory in the field of information technology.

Content

What do sample space and random variable mean and how is probability defined?
Which kind of predefined distributions are there for random variables?
What is meant by information theory?
What is meant by maximum entropy principle?
How are probability and information theory applied in information technology and decision-making?

Evaluation

Students can
a. use professional vocabulary and concepts in an expert way in different situations.
e. choose appropriate models, methods, software and techniques according to the purpose and justify these choices.

Course material

Learning materials include selected book chapters for core theory, curated online resources, and the instructor’s slide decks. Each lecture is paired with a guided exercise notebook so students can immediately apply the concepts to real datasets.

Study forms and methods

The course combines theoretical lectures, guided readings and short videos with hands-on exercises. Lectures and materials introduce the key statistical concepts, while practical sessions focus on applying methods to real datasets using software tools. Students are expected to prepare through readings and videos, then practice and deepen their understanding in exercises and project work.

Timing of exams and assignments

A mid-term exam is scheduled halfway through the course and a final exam at the end. After every lecture students receive a homework assignment, usually due before the next session.

Student workload

The course is worth 5 ECTS, which corresponds to about 135 hours of student work. Of this, 21 hours are contact teaching through 14 lectures of 1.5 hours each. The remaining workload is completed as independent study, including homework assignments after each lecture, and exam preparation.

Course part description

The course is divided into two integrated parts. Part I – Descriptive Statistics (weeks 1–5) introduces data types, numerical and graphical summaries, and exploratory data analysis so that students can organise, visualise, and clean real datasets. Part II – Inferential Statistics (weeks 6–12) builds on that foundation with a short probability review, sampling theory, point and interval estimation, hypothesis testing, simple regression, ANOVA, and an introduction to non-parametric alternatives. Together these parts provide a complete pathway from describing the data you have to drawing reliable conclusions about the population you cannot directly observe.

Evaluation scale

1-5

Assessment methods and criteria

Assessment is based on exams and assignments. The grading scale is 0–5.

0 (Fail): Student shows insufficient understanding of basic concepts; major errors in calculations or interpretations.

1 (Sufficient): Basic concepts of descriptive and inferential statistics are recognised, but application is limited and reasoning contains gaps.

2 (Satisfactory): Student can apply standard methods (summaries, simple tests, intervals) with some accuracy but lacks deeper interpretation.

3 (Good): Student applies methods correctly, interprets results appropriately, and shows understanding of both descriptive and inferential tools.

4 (Very Good): Student demonstrates strong mastery, connects different methods (e.g., linking probability to inference), and can justify choices.

5 (Excellent): Student shows comprehensive and critical understanding, applies methods flexibly to new contexts, and communicates findings clearly and professionally.

Qualifications

Attending the course requires basic knowledge of sets, Boolean algebras and calculus.