Università Roma Tre

1. Introduction to combinatorial analysis.

2. Introduction to Probability.

3. Conditional probability, Bayes' formula. Independence.

4. Discrete random variables. Bernoulli, binomials, Poisson, geometric, hipergeometric, negative binomial.
Expected value.

5. Continuous random varaibles. Uniform, exponential, gamma, gaussian.
Expected value.

6. Independent variables and joint laws.
Sum of two or more independent random variables. Poisson process. Maxima and minima of independent random variables.

7. Limit theorems. Markov and Chebyshev inequalities.Weak law of large numbers. Generating functions and a sketch of proof of the central limit theorem.

Sheldon M. Ross, Calcolo delle Probabilita'. Apogeo, (2007).



F. Caravenna, P. Dai Pra, Probabilita'. Springer, (2013).

Combinatorics, assioms of probability, conditional probability and independence, discrete random variables. Continuous random variables, density and distribution functions. Independence and joint laws. Relation between exponential distribution and Poisson distribution. Limit theorems, moment generating functions and sketch of central limit theorem.

- S. Ross, Calcolo delle probabilita' (Apogeo Ed.)
- F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.)
- W. Feller, An introduction to probability theory and its applications (Wiley, 1968).