## PROBABILITY AND STATISTICS PROBABILITÀ E STATISTICA MATEMATICA

A.Y. Credits
2021/2022 6
Lecturer Email Office hours for students
Alessia Elisabetta Kogoj tuesday and wednesday 11:00-13:00 and on demand
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

### Assigned to the Degree Course

Applied Informatics (L-31)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location
Date Time Classroom / Location

### Learning Objectives

The course is meant to provide the basics of the theory of probability, random variables and distribution functions as well as the main concepts of inferential statistics and hypothesis testing.

### Program

01. Probablity calculus:
01.01 Probability space, events.
01.02 Conditional probability. Independence.
01.03 Law of total probability (and its proof).
01.04 Bayes rule (and its proof).
01.05 Examples, problems and applications.

02. Random variables:
02.01 Independent random variables.
02.02  Expected value, variance and their properties.

03. Discrete random variables:
03.01 Probability Mass function.
03.02 Special discrete distributions: Bernoulli, binomial and Poisson distributions.
03.03 Poisson distribution as an approximation for binomial: theorem and proof.
03.04 Geometrical distributions and negative binomial distributions.

04. Continuous random variables:
04.01 Probability density function and distribution function.
04.02 Special continuous distributions :  Uniform distribution, Exponential distribution, Gaussian distributions.

05.  Limit theorems:
05.01 Markov inequality (and its proof).
05.02 Law of large numbers (and  its proof).
05.03 Central limit theorem.

### Bridging Courses

Calculus (suggested not mandatory).

### Learning Achievements (Dublin Descriptors)

Knowledge and understanding: the student will be acquainted with the basis of the mathematical theory of Probability and of the Inferential Statistics.

Applying knowledge and understanding: the student will be able to theoretically analyse problems where stochastic variability plays a fondamental role.

Making judgements: the student will be able to choose among several approaches the suitable solution to probabilistic problems.

Communication skills: the student will be able to communicate probabilistic informations by use of the techniques of the differential and integral calculus.

Learning skills: the student will learn the methodology to be used in the mathematical formulation of empirical phenomena.

### Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

### Teaching, Attendance, Course Books and Assessment

Teaching

Theory lectures and exercises, both face-to face and on-line.

Attendance

Course attendance is not mandatory.

Course books

P. Baldi, "Calcolo delle Probabilità e Statistica", McGraw-Hill.

S. Ross: ”Probabilità e statistica per l’ingegneria e le scienze”, APOGEO.

Assessment

Written and oral exam.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

### Additional Information for Non-Attending Students

Teaching

Theory lectures and exercises, both face-to face and on-line.

Attendance

Course attendance is not mandatory.

Course books

P. Baldi, "Calcolo delle Probabilità e Statistica", McGraw-Hill.

S. Ross: ”Probabilità e statistica per l’ingegneria e le scienze”, APOGEO.

Assessment

The exam of Probability and Statistics  consists of a written exam and an oral one, both of them mandatory.

The written exam, to carry out in two hours, consists of exercises related to the topics of the course. The written exam is passed if the mark is, at least, 15/30. During the written exam it is not allowed to use textbooks, workbooks or notes. Moreover, it is not allowed to use scientific calculators and mobile phones, under penalty of disqualification.

The oral exam consists of a discussion related to the topics of the course.  The oral exam can be taken only if the written one has been passed. If so, the oral exam can be taken only in the same call in which the written exam has been passed or in the other calls of the same session.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

### Notes

The course offers additional e-learning facilities on the Moodle platform > elearning.uniurb.it

 « back Last update: 17/01/2022

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