The objective of the course is to introduce the language of probability and to describe the simplest stochastic models for the evolution of phenomena over time. The knowledge acquired will serve as a foundation for future courses and work, in particular those focused on the evaluation of insurance and financial products, as well as applications to financial markets and the pricing of derivatives.

Lectures will be held on:

• Monday 2-4pm, Auletta 1st floor
• Tuesday 12-2pm, Auletta 1st floor
• Thursday 2-4pm, Aula Fanfani 5th floor
  

The syllabus is the following:

• Week 1: Events and probability.
• Week 2: Conditional probability. Independence. Discrete random variables.
• Week 3: Functions of discrete random variables. Expectations of discrete random variables.
• Week 4: Multivariate discrete distributions and independence.
• Week 5: Conditional expectations.Probability generating functions.
• Week 6: Distribution functions. Continuous random variables. Density functions. Expectations of continuous random variables
• Week 7: Random vectors. Marginal distributions. Independence
• Week 8: Sums of random variables. Change of variables. Conditional density
• Week 9: Multivariate normal. Moments and covariance of continuous random variables
• Week 10: Moment generating functions, The main limit theorems
• Week 11: Random walks, Markov chains: introduction
• Week 12: Markov chains: limit theorems