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1. Discrete probability space, combinatorics formulae, discrete uniform probability, sampling with replacement and without replacement. Bernoulli sequence.
2. General probability space, probability axiomatics. Probability properties.
3. Conditional probability. Events independence. Total probability. Bayes formula.
4. Random variables. Distribution and distribution function. Distribution function properties. Main distributions. Discrete and continuous random variables. Probability density.
5. Random variables numerical characteristics: expectation, variance, standard deviation, moments, correlation coefficient. Chebyshev inequality.
6. Multivariate random variables, random variables independence, joint distributions, conditional and marginal distributions.
7. Types of covergence of random variable sequences: convergence in probability and convergence in distribution. Bernoulli, Chebyshev and Khinchyn laws of large numbers.
8. Moivre-Laplace and Poisson theorems and their applications. The central limit theorem.
9. Point estimation. Consistent, biased and unbiased estimators. Maximum likelihood and moments methods.
10. Point estimation. Consistent, biased and unbiased estimators. Maximum likelihood and moments methods.
11. Estimators comparison in the sense of mean square deviation. Estimators efficiency.
12. Main statistical distributions (chi-squqre, Student, Fisher).
13. Interval estimation. Exact and asymptotic confidence intervals. Confidence intervals for normal distribution parameters.
14. Hypotheses testing. First kind and second kind error. Power of a statistical test. Parametrrical hypotheses testing. Criterion chi-square.
15. Nonparametric hypotheses testing: chi-square like nonparametric kriterion, criterion omega-square. Kolmogorov criterion.
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