First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
INTRODUCTION TO PROBABILITY (Ult. numero di matricola pari)
SCP4063485, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC2095, Degree course structure A.Y. 2014/15, A.Y. 2017/18
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO PROBABILITY
Website of the academic structure
Department of reference Department of Statistical Sciences
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge DAVID BARBATO MAT/06
Other lecturers MARKUS FISCHER MAT/06

Course unit code Course unit name Teacher in charge Degree course code
SCP4063485 INTRODUCTION TO PROBABILITY (Ult. numero di matricola pari) DAVID BARBATO SC2094

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/06 Probability and Mathematical Statistics 9.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 26 24.0 No turn
Lecture 7.0 56 119.0 No turn

Start of activities 26/02/2018
End of activities 01/06/2018
Show course schedule 2020/21 Reg.2014 course timetable

Examination board
Examination board not defined

Prerequisites: Basic calculus for functions of one real variable.
Target skills and knowledge: The course is concerned with the fundamental notions of Probability, whose aim is the modeling of random phenomena. The emphasis is on basic general concept; the aim is to develop the capability of applying these concept to concrete and relevant examples.
Examination methods: Written exam. The teacher could require, in special cases, to complete the exam with an oral part.
Assessment criteria: The exercises have the aim of verifying the full understanding of basic notion of probability, as well as the capability of applying them to concrete examples. Clarity and coherence of the solutions will also determine the final evaluation.
Course unit contents: Random experiments, sample space, probability.
Sample space with finitely many elements, combinatorics.
Conditional probability and independence.
Discrete random variables, discrete density and distribution.
Multivariate discrete random variables, joint and marginal densities. Independence of discrete random variables.
Expectation for discrete random variables. Variance, covariance, moments.
Basic discrete distributions: Binomial, Hypergeometric, Geometric, Negative Binomial, Poisson.
Conditional density and conditional expectation for discrete random variables.
Absolutely continuous random variables and their expectation.
Basin continuous distributions: Uniform, Gamma Normal.
Multivariate continuous random variables, joint densities, independence.
Conditional density and conditional expectation for absolutely continuous random variables.
Law of large numbers and central limit theorem. Normal approximation.
Planned learning activities and teaching methods: The presentation of theoretical notions is complemented by examples and exercises.
Textbooks (and optional supplementary readings)
  • Sheldon M. Ross, Calcolo delle probabilit√†. --: Apogeo, 2013. Cerca nel catalogo