Probability spaces. Conditional probability. Formula of total probability. Bayes formula. Independent events. Elements of combinatorics. Introduction to random variables. Distribution function. Discrete random variables and discrete distributions in common use (hypergeometric, binomial, geometric, negative binomial, Poisson). Multidimensional discrete random variables. Independent discrete random variables. Mathematical expectation, moments, variance and covariance for discrete random variables. Cebichev Inequality. Linear regression. Continuous random variables and continuous distributions in common use (uniform, exponential, normal, gamma). Poisson process. Mathematical expectation, moments and variance for continuous random variables. Law of large numbers. Central limit theorem. Normal approximation.
The course belongs to the field of mathematics, and in particular of probability and statistics. It aims at introducing the student to the comprehension of random phenomena at one side and at giving the methodological and analytical tools both as support for later courses and as intrinsic ability, on the other side. The concepts of risk and probability give the analytical and theoretical devices for the investigation of random events, as the introduction to basic statistics gives the methodology for the exploration of sampled random quantities.
KNOWLEDGE AND UNDERSTANDING:
Students will be able to understand theory and solve exercises.
APPLYING KNOWLEDGE AND UNDERSTANDING:
Students will be able to understand how to use theory to solve exercises.
Students will be able to explain the procedures used in the solutions of exercises, possibly by referring to some theoretical results.
Students will have the ability to master the mathematical concepts used.
Students will be able to make connections between different theoretical issues.