84608 - Probability

Learning outcomes

By the end of the course module the student should know the basic tools of probability calculus, with a special focus on their role in the statistical analysis. In particular, the student should be able to: - compute the probability of events, by using the axioms and the fundamental theorems of probability calculus - identify the main discrete and continuous random variables

Course contents

• Probability spaces and Kolmogorov axioms
  
• Conditional probability and indpendent events
  
• Law of total probability and Bayes' formula
• Discrete random variabes: probability function, expected value and variance. Probabililistic models: Bernoulli, Binomial, Poisson, Geometric
• Continuous random variables: probability density function and distribution function, expected value and variance. Probabilistic models: Uniform, Normal, Gamma, Student.
  
• Law of large numbers and applications
  
• Central limit theorem and applications
  

Readings/Bibliography

Lecture notes.

Suggested readings:

• Paolo Baldi, Calcolo delle Probabilità, II edizione, McGraw-Hill,
  Milano, 2011

Teaching methods

Lectures and tutorials

Assessment methods

One-hour written exam, articulated in a series of 2 exercises each with a maximum grade of 15 points. Every exercise attains to elements of the syllabus covered during the course lectures. Online exams will be supported by the softwares Teams, Zoom and EOL (https://eol.unibo.it/)

Teaching tools

Slides and exercises with solutions

Office hours

See the website of Alberto Lanconelli