1. Discrete random vectors.
1.1. Joint, marginal and conditional distributions.
1.2. Independence.
1.3. Functions of random vectors.
1.4. Expected value and variance, conditional expectation.
1.5. Discrete multivariate models.
2. Continuous Random vectors.
2.1. Joint, marginal and conditional distributions.
2.2. Independence. Functions of random vectors.
2.3. Change of variable. Expected value and variance.
2.4 Conditional expectation.
2.5. Multidimensional normal distribution.
2.6 Distribution related to the Normal distribution (chi-square and t-student)
3. Generating functions and convergence of random variables.
3.1. Markov inequality and convergence in probability.
3.2. Laws of large numbers and Monte Carlo Method.
3.3. Generating functions and moments.
3.4. Convergence in distribution and Central Limit Theorem