1. Outcomes, event, probabilities.

1.1 Sets of outcomes, events, axioms of probability.

1.2 Conditional probability, independence.

2. Random variables.

2.1 Random variables and their distributions.

2.2 Discrete random variables..

2.3 Continuous random variables.

2.4 Functions of random variables.

3. Joint distributions.

3.1 Discrete joint distributions.

3.2 Continuous joint distributions.

3.3 Conditional distributions.

3.4 Independence.

4. Expectation.

4.1 Definition of expectation.

4.2 Variance and covariance.

4.3 Conditional expectation.

5. Central limit theorem.

5.1 Convergence of distributions.

5.2 Central limit theorem.

6. Sampling.

6.1 Simple random sampling.

6.1 Standard error and confidence intervals.

6.2 Stratified sampling.

7. Parameter estimation.

7.1 Statistical models.

7.1 Estimators, standard errors.

7.2 Maximum likelihood method.

7.3 Asymptotic properties.

8. Hypothesis testing.

8.1 Basic idea, Neyman-Person.

8.2 Test statistics and its distribution.

8.3 Size and power of the test.

8.4 Likelihood ratio test.

9. Linear regression.

9.1 Definition of regression model.

9.2 Parameter estimation.

9.3 Gauss-Markov theorem.