Content of the Lectures

Statistics I

The course Statistics I contains basic techniques of descriptive data analytics and a profound introduction to probability calculus as well as random variables.

content overview:

1. introduction
2. descriptive statistics
   1. basic concepts
   2. univariate statistics
   3. bivariate statistics
3. introduction to probabilities
   1. probability
   2. conditional probability
4. random variables and vectors
   1. definition and distribution
   2. univariate statistics
   3. bivariate statistics
   4. multivariate extensions
5. important distributions
   1. discrete distribution models
   2. continuous distribution models
   3. approximation of distributions

Statistics II

The course Statistics II  provides an introduction to statistical estimation and testing methods as well as multiple linear regression.

content overview:

1. sampling theory
   1. introduction statistical inference and short revision
   2. sampling distributions and key parameters
2. statistical estimation procedures
   1. estimation functions
   2. construction of estimation functions
   3. interval estimation
3. statistical testing procedures
   1. general test
   2. testing the mean
   3. formulating hypotheses for one-sided test
   4. testing the success probability
   5. testing the difference between two means
   6. Chi-square goodness of fit test
   7. Chi-square independence test
   8. power function
4. regression
   1. the single and multiple regression problem
   2. estimation of the regression parameters
   3. goodness of fit
   4. statistical test of the regression coefficients
   5. confidence intervals