1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To introduce students to the basic notions of probability theory.

COURSE DESCRIPTION AND SYLLABUS:
1. Basic probability notions. Events, sample space, probability, etc. (3 hours)
2. Discrete probability space. Finite case. Laplace model. Countable case. Elements of combinatorics. (2 hours)
3. Geometric probability. (2 hours)
4. Conditional probability. Independence. Bayes formula. Borel 0-1 law. (2 hours)
5. Repeated trials. Product space. Independent case and conditioned case. (3 hours)
6. Bernoulli trials. Binomial distribution. Discrete distributions. Poisson and Moivre-Laplace theorems. (6 hours)
7. Discrete random variables. Distribution functions, density. Multidimensional case. Independent variables. Basic formulas. Expectation, variance, Čebišev inequality, and related concepts. Convergence. Weak and strong laws of large numbers. (9 hours)
8. Continuous random variables. Examples, density functions, expectations, and other basic concepts. Multidimensional case. Emphasis is on basic examples: Gaussian (normal), gamma, Chi-square distribution, Fisher, etc. Central limit theorem (no proofs) with applications. Conditional density. (12 hours)
9. Poisson process. (3 hours)

Enrollment :
Passed : Mathematical analysis 2

Mandatory course - Regular study - Mathematics