Courses in mathematical statistics - course RUB 28,480. from Online school TutorOnline, training 64 ac. hours, Date: December 2, 2023.

Math statistics.

Topic 1. Selective method - 9 hours.

1. Goals and methods of mathematical statistics.
2. Sampling method.
3. General and sample populations.
4. Selection methods.
5. Statistical distribution of the sample.
6. Discrete and interval variation series.
7. Empirical distribution function.
8. Polygon and histogram.
9. Distribution density of the trait.

Topic 2. Statistical estimates of distribution parameters – 14 hours.

1. Sample characteristics of random variables.
2. The concept of a point estimate.
3. Unbiased, consistent, and efficient estimates.
4. Point estimates for the general mean (expectation), general variance, and general standard deviation.
5. The theory of point estimates.
6. Likelihood function.
7. Maximum likelihood method, method of moments.
8. The concept of interval estimation.
9. The theory of interval estimation.
10. Confidence interval and confidence probability.
11. Construction of confidence intervals for estimating sample parameters from a normal population.
12. Reliability of the confidence interval.
13. Interval estimation of the mathematical expectation of a normal distribution with a known variance.
14. Interval estimation of the mathematical expectation of a normal distribution with unknown variance.

Topic 3. Statistical testing of hypotheses - 12 hours.

1. Statistical hypothesis and statistical test.
2. Errors of the 1st and 2nd kind.
3.Level of significance and power of the criterion.
4. The principle of practical certainty.
5. Finding critical areas.
6. Testing hypotheses about the coincidence of distribution parameters.
7. Comparison of means and variances of normal populations.
8. Testing hypotheses about the type of distribution.
9. Nonparametric goodness-of-fit tests.
10. Pearson's theorem.
11. Chi-square test, Kolmogorov test.
12. Examples of using the chi-square test and the Kolmogorov test.

Topic 4. Correlation analysis - 23 hours.

1. Basic provisions.
2. Correlation field.
3. Correlation table.
4. Finding the parameters of the sample linear mean square regression equation.
5. Sample correlation coefficient.
6. Correlation relationship.
7. Multivariate correlation analysis.
8. Rank correlation.
9. Spearman and Kendall sample rank correlation coefficient.
10. Examples of application of the Spearman and Kendall sample rank correlation coefficient.
11. Functional and statistical dependencies.
12.Group averages.
13. The concept of correlation dependence.
14. The main tasks of correlation theory: determining the form and assessing the closeness of the connection.
15. Types of correlation (paired and multiple, linear and nonlinear).
16. Regression equations.
17. Linear regression.
18. Least square method.
19. Determining the parameters of regression lines using the least squares method.
20. Sample correlation coefficient, its properties.
21. Nonlinear regression.
22. Testing the hypothesis about the significance of the correlation coefficient.
23.Checking the optimality and adequacy of the chosen form of connection between two random variables.

Topic 5. Regression analysis - 6 hours.

1. Basic principles of regression analysis.
2. Construction of a mathematical model.
3. Regression equations, their approximations.
4. Assessing the significance of regression coefficients.
5. Checking the adequacy of the model.
6. Application examples.