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Probability theory

General data

Course ID: 1000-712bRPR
Erasmus code / ISCED: 11.102 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title: Probability theory
Name in Polish: Rachunek prawdopodobieństwa
Organizational unit: Faculty of Mathematics, Informatics, and Mechanics
Course groups: Obligatory courses for 2nd year Bioinformatics
ECTS credit allocation (and other scores): 5.00 Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
Language: Polish
Type of course:

obligatory courses

Short description:

The course is an introduction to the basic concepts and methods of the probability theory. The material includes the notion of probability, Kolmogorov’s axioms, conditional probability and independence, overview of basic discrete models of probability theory, basic discrete and continuous probability distributions, parameters of probability distributions, laws of large numbers, Central Limit Theorem, Markov chains, elements of information theory.

Full description:

1. Probabilistic models of experiments, Kolmogorov’s axioms.

2. Basic combinatorial schemes, classical probability, geometric probability.

3. Conditional probability.

4. Independence of events, Bernoulli trials.

5. Random variables and random vectors, discrete and continuous; distribution (law) of a random vector, cumulative distribution function, probability density function.

6. Parameters of probability distributions: expected value, variance, moments, median, quantiles, covariance matrix.

7. Independence of random variables, criteria of independence for discrete and continuous random variables. Distribution of a sum of independent random variables, convolution of measures.

8. Overview of basic probability distributions.

9. Basic probabilistic inequalities.

10. Laws of large numbers: weak law of large numbers, Kolmogorov’s Strong Law of Large Numbers.

11. Central Limit Theorem.

12. Markov chains. Classification of states. Ergodic theorem for Markov chains.

13. Elements of information theory: Shannon’s entropy, mutual information, interpretation and connections with coding theory.

Bibliography:

Rachunek Prawdopodobieństwa dla (Prawie) Każdego - Jakubowski Jacek, Sztencel Rafał, SCRIPT Wydawnictwo, 2006 [in Polish]

Learning outcomes:

After completing the course, the student:

• knows the basic concepts and methods of probability theory: Kolmogorov's axiomatics, conditional probability, independence, continuous and discrete distributions, distribution parameters, laws of large numbers and the central limit theorem, Markov chains, elements of information theory

• is able to understand the basic probabilistic arguments used in the literature related to bioinformatics

• understands the nature of probabilistic modeling of natural phenomena

• can build and analyze probabilistic models of simple random phenomena, using the basic tools and theorems of the probability theory

• is ready to further study the theory of statistics and data processing

Assessment methods and assessment criteria:

written exam

Classes in period "Winter semester 2024/25" (past)

Time span: 2024-10-01 - 2025-01-26
Selected timetable range:
Go to timetable
Type of class:
Classes, 45 hours more information
Lecture, 30 hours more information
Coordinators: Katarzyna Pietruska-Pałuba
Group instructors: Stanisław Cichomski, Katarzyna Pietruska-Pałuba
Students list: (inaccessible to you)
Credit: Examination

Classes in period "Winter semester 2025/26" (future)

Time span: 2025-10-01 - 2026-01-25

Selected timetable range:
Go to timetable
Type of class:
Classes, 45 hours more information
Lecture, 30 hours more information
Coordinators: Katarzyna Pietruska-Pałuba
Group instructors: Stanisław Cichomski, Katarzyna Pietruska-Pałuba
Students list: (inaccessible to you)
Credit: Examination
Course descriptions are protected by copyright.
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