- Docente: Paolo Negrini
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
After completing the course, the student knows some important probabilistic tools and the basic methods of mathematical statistics. he can apply in real situations the probabilistic and statistical methods acquired.
Course contents
A brief history of the origins of probability. Classical problems of discrete probability. The classical theory, frequentist subjective. Examples. Analysis of exercises contained in the texts for adoption in secondary schools or proposed in the written tests the final examination. Life tables: significance of their data and applications. Elements of actuarial mathematics. Elements of statistical inference: estimators, confidence intervals; statistical hypothesis testing. Cochran's theorem. The test "Chi Square" for the comparison of distributions and for independence. Markov chains. Transition matrix; transient and recurring states. Classic examples: gambler's ruin, birth and death. Average time for the fall of the player. Probability of absorption within a set time. Stationary distributions. Irreducible Markov chains or regular The Markov-Kakutani and Markov theorems.
Readings/Bibliography
Nicolò Pintacuda: Primo corso di probabilità. Muzzio, 1983 Paolo Baldi: Calcolo delle probabilità e statistica. McGraw-Hill 1998.
Lecture notes written by the teacher
Teaching methods
frontal lessons
Assessment methods
written and oral examination
Office hours
See the website of Paolo Negrini