Syllabus
* Probability
- random trial, random event, probability(classical, geometrical), recapitulation of elements of combinatorics
- independence of random events, conditional probability, complete probability theorem, the theorem of Bayes
- random variables and distribution of probability, expected value, variance, other characteristics
- discrete and continuos distributions (alternative, binomial, hypergeometric, geometric, Poisson, uniform, exponential), probability density, distribution function
- random vectors, joint and marginal probability density and distribution function
- independence of random variables, covariance, corellation
- operation with random variables, Law of the great numbers, central limit theorem, normal distribution, distribution chi-square, Student, Fischer
* Statistics
- random sample, parameter estimate, testing hypotheses principle, statistical discrepancy
- basic types of statistic tests (t-test, one-sample, two-sample, corellation coefficient)
- linear regression, method of least squares
- analysis of variance
- contingency table, some other tests (McNemar), Pearson's chi-square test
- non-parametric methods (sign test, Wilcoxon test, Spearmann coefficient)
- descriptive statistics, data processing
Annotation
Random trial, random event, probability, distribution of probablity, probability density, distribution function. Operations with random variables, Law of great numbers, central limit theorem.
Distribution: normal, chi-square, Student. Testing hypotheses, statistical tests, data processing