1. Random variables and random vectors.

1.1 Outcomes, events, probabilities, conditional probabilities.

1.2 Random variables and their distributions.

1.3 Random vectors and their distributions.

1.4 Conditional distributions and independence.

1.5 Functions of random variables and random vectors.

1.6 Expectation, variance and covariance.

1.7 Conditional expectation.

1.8 Convergence of random variables, central limit theorem.

1.9 Multivariate normal distribution.

2. Estimation.

2.1 Statistical models, parameters, estimators.

2.2 Sampling distributions, standard errors, confidence intervals.

2.3 Properties of estimators, consistence.

2.4 Maximum likelihood estimation, asymptotic properties.

3. Hypothesis testing.

3.1 Basic idea, Neyman-Pearson setup.

3.2 Test statistics and its distribution.

3.3 The likelihood ratio test.

3.4 Size and power of the test.

4. Regression.

3.1 Definition of the regression model, examples.

3.2 Least squares estimation, Gauss-Markov theorem.

3.3 The linear hypothesis.