Probability theory 1000-712bRPR
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.
Type of course
Course coordinators
Term 2024Z: | Term 2023Z: |
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 criteria
written exam
Bibliography
Rachunek Prawdopodobieństwa dla (Prawie) Każdego - Jakubowski Jacek, Sztencel Rafał, SCRIPT Wydawnictwo, 2006 [in Polish]
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: