84608 - Probability

Academic Year 2017/2018

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Statistics, Economics and Business (cod. 8876)

Learning outcomes

At the end of this course, the student knows the basic tools of probability calculus, with a special focus at their role in the statistical analysis. In particular, the student should be able: - to compute the probability of random events, by using the axioms and the fundamental theorems of probability calculus; - to treat the main discrete and continuous random variables.

Course contents

Random experiments, event space and random events

Probability function and criteria for measauring a probability value

Kolmogorov axioms and probability theorems

Conditional probability

Bayes-Laplace theorem

Discrete random variables: probability mass function and cumulative function. Bernoulli, Binomial, Poisson and Geometric distributions

Continuous random variables: probability density function and cumulative function. Gaussian, Chi-square, t distributions

Central limit theorem

Readings/Bibliography

  • G. Cicchitelli, Statistica, Principi e Metodi, seconda edizione, Pearson Education Italia, 2012.
  • A. Montanari, P. Agati, D.G. Calò, Statistica con esercizi commentati e risolti, Casa Editrice Ambrosiana, Milano, 1998.
  • L. Stracqualursi et al., Test di Statistica a risposta multipla, 2017 (https://www.amazon.it)

Teaching methods

Lectures. Tutorial application.

Assessment methods

The aim is to check that the student has learnt the basic tools of the subject, as well as his/her critical skills in choosing the most adequate tool to solve a given problem.

Written exam (compulsory), consisting of exercises and multiple choice tests covering the total program of the course (1 hour). Some examples are available in the textbook by Montanari et al. and Stracqualursi et al., suggested in the Section "Reading/Bibliography".

The evaluation is expressed in marks out of 30.

Teaching tools

Blackboard; PC; videoprojector; computer laboratory
Teaching material is available at http://campus.unibo.it/ (download is allowed only to University of Bologna students).

Office hours

See the website of Patrizia Agati