Syllabus
- Introduction of measure (Jordan, Lebersque, Hausdorff), set systems, measurability, measure properties.
- Independence of random events, conditional probability, complete probability theorem, the Bayes theorem.
- Random variable and ots distribution of probability, charakteristics, discrete and continuous distributions (alternative, binomial, hypergeometric, geometric, Poisson, uniform, exponential), probability density, distribution function.
- Random vectors, conjugate and marginal density and distribution function, independence of random variables, covariance, corellation.
- Operation with random variables, Law of great numbers, central limit theorem (Moivre - Laplace theorem), normal distribution, distribution chí-square, Student and Fischer.
Annotation
Measure and measurability, probability measure, random events, random variables and their distribution, normal distribution.