Probability and Statistics II (FSI-SP2)

Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing all written exams, and semester assignment acceptance. Preparing and defending a project.

Examination: written form of the exam (50 points) and oral part (50 points): a practical written part (4 tasks related to random vectors, conditional distribution, multivariate normal distribution, regression analysis, correlation analysis, categorical data analysis); theoretical oral part (4 tasks related to basic notions, their properties, sense and practical use, and proofs of two theorems); evaluation according to the total number of points (scoring 0 points for any of 4 practical tasks or whole theoretical part means failing the exam): excellent (90 - 100 points and both proofs), very good (80 - 89 points and both proofs), good (70 - 79 points and one proof), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).

Participation in the exercise is mandatory and the teacher decides on the compensation for absences.

Random vector, moment characteristics.
Conditional distribution.
Characteristic function.
Multivariate normal distribution - properties.
Distribution of quadratic forms.
Linear regression model (LRM) and parameter estimates in LRM.
Testing hypotheses concerning linear regression model.
Special cases of LRM (regression line, regression parabola, polynomial regression, ANOVA models).
Weighted regression, an introduction to regression diagnostic and linearized regression model.
Correlation analysis
Goodness of fit tests with known and unknown parameters
Introduction to categorical data analysis (chi-square test, measures of association, Fisher factorial test).