Probability and Statistics
Aims of the course
This course aims to develop students’ abilities to design and carry out methodologically sound and practically relevant empirical research of qualitative nature.Course syllabus
Random variables and their distributions. Transformations of random variables.
Expectation and conditional expectation.
Convergence of random variables, central limit theorem.
Distributions derived from the normal distribution.
Survey sampling.
Estimation of parameters, properties of estimators, asymptotic properties of estimators.
Hypothesis testing, Wilk’s theorem.
Sufficiency, factorization theorem, optimal theory of estimation and hypothesis testing.
Linear models, Gauss-Markov theorem, general linear hypothesis, generalizations, prediction, diagnostics.
Multivariate normal distribution, conditional distribution, quadratic forms.
Abstract conditional expectation, optimal forecasting.
