79222 - PROBABILITY I

Conoscenze e abilità da conseguire

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 and compute their expected values and variances - analytically treat univariate and bivarate random variables.

Contenuti

• Probability spaces and Kolmogorov axioms
  
• Conditional probability, Law of Total Probability and Bayes' formula
• Independent events
  
• Random variables and distribution functions, discrete and continuous random variables, expected value, variance and covariance
  
• Discrete models: Bernoulli, Binomial, Hypergeometric, Poisson, Geometric
• Continuous models: Uniform, Gaussian, Gamma, Student, Fisher.
  
• Law of Large Numbers and applications
  
• Central Limit Theorem and applications

Testi/Bibliografia

Alberto Lanconelli, Introduction to Probability Theory (2023) ISBN-13: ‎979-8850457037

Metodi didattici

Regular lectures and tutorials

Modalità di verifica e valutazione dell'apprendimento

The Probability I course is part of the integrated course Statistics and Probability. The course Statistics and Probability consists in a written and an oral assessment. The written assessment lasts 2 hours and is composed of two parts related to Statistics and Probability respectively.

For the Probability I written assessment the student is required to solve 2 exercises each with a maximum grade of 15 points. The written test is aimed at assessing the student's ability to use the definitions, properties and theorems of probability theory in solving theoretical exercises. Every exercise attains to elements of the syllabus covered during the course lectures.The mark for the written assessment will be the average of the mark in Statistics and the mark in Probability.

The oral assessment involves questions on the theory of both Statistics and Probability. Only the students who have passed the written exam can sit the oral one. Students can take the written exam in one sitting and the oral exam in a different one.

In case of online exam, this will be supported by the softwares Teams, Zoom and EOL (https://eol.unibo.it/)

Strumenti a supporto della didattica

Exercises with solutions

Orario di ricevimento

Consulta il sito web di Alberto Lanconelli