1. Probability spaces and their properties. Finite, uniform probability spaces. Combinatorics. extractions without replacement.
2. Conditional probability and its properties. Bayes formula. Independent events and conditionally independent events. Bernouli trials.
3. Discrete random variables: binomial, hypergeometric, geometric and Poisson laws.
4. Continuous random variables: uniform, exponential and Gaussian laws. Distribution function.
5. Expectation and its properties. Variance. Quantiles.
6. Joint laws of random variables: marginals, independence, conditional density. Density of the sun of two random variables. Sum of independent Gaussian random variables.
8. Joint Gaussian distributions.
9. Law of large numbers and Central Limit Theorem.