First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC03106737, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
SC1167, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination PROBABILITY AND STATISTICS
Website of the academic structure
Department of reference Department of Mathematics
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 FRANCESCA COLLET MAT/06

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/06 Probability and Mathematical Statistics 6.0

Course unit organization
Period Second semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 16 34.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
4 a.a 2019/2020 01/10/2019 28/02/2021 COLLET FRANCESCA (Presidente)
FONTANA CLAUDIO (Membro Effettivo)
3 a.a 2018/2019 01/10/2018 28/02/2020 COLLET FRANCESCA (Presidente)
FONTANA CLAUDIO (Membro Effettivo)

Prerequisites: Familiarity with the basic notions of analysis, linear algebra and combinatorics. The courses "Analisi matematica" and "Algebra e matematica discreta" cover all the necessary prerequisites.
Target skills and knowledge: The student will acquire a basic knowledge of probability theory and inferential statistics. Those that will pass the exam will be able to build simple probabilistic models of uncertain phenomena and carry out the necessary probabilistic and/or statistical computations.
Examination methods: 3 hour written test (closed book).
Assessment criteria: The student will have to master the theoretical concepts and show his ability to apply them to solve problems of probability and statistics of appropriate difficulty.
Course unit contents: Probability theory. Axioms and their elementary consequences. Examples of discrete, finite, and uniform probability spaces. Combinatorics. Conditional probability. Law of total probability and Bayes formula. Independent events. Discrete random variables. Probability mass function. Moments: expectation, variance and higher order moments. Examples of discrete random variables: Bernoulli, binomial, geometric and Poisson distributions. Poisson limit theorem. Discrete random vectors. Joint and marginal discrete densities. Expectation of real functions of discrete random vectors. Covariance. Independent discrete random variables. Absolutely continuous random variables. Probability density function and distribution function. Moments: expectation and variance. Examples of absolutely continuous random variables: uniform, exponential and normal distributions. Limit theorems. Weak law of large numbers. Monte Carlo method. Central limit theorem. Normal approximation.

Descriptive statistics. Qualitative and quantitative data, relative frequencies, graphical methods. Empirical indices: location, centrality, dispersion, shape. Correlation between variables: regression line, covariance and correlation coefficient.

Inferential statistics. Estimators. Confidence intervals.
Planned learning activities and teaching methods: Traditional lectures. A typical lecture is aimed at transmission of theoretical contents, illustration of examples and solution of exercises. Through the moodle platform homework assignments are proposed weekly and then solved.
Additional notes about suggested reading: The lectures cover all the topics on which the exam is based. The moodle platform contains several teaching aids: additional references, notes and several sheets of exercises with their solutions.
Textbooks (and optional supplementary readings)
  • Finesso, Lorenzo, Lezioni di probabilit√†. Padova: Libreria Progetto, 2017. Cerca nel catalogo
  • Ross, Sheldon M., Introduzione alla statistica. Milano: Apogeo, 2008. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex