## PROBABILITY AND STATISTICS PROBABILITÀ E STATISTICA MATEMATICA

#### PROBABILITY AND STATISTICS PROBABILITÀ E STATISTICA MATEMATICA

A.Y. Credits
2016/2017 6
Lecturer Email Office hours for students
Alessia Elisabetta Kogoj wednesday 11:00-13:00 and on demand
Teaching in foreign languages
Course with online activities entirely in a foreign language English
For this course offered in face-to-face/online mixed mode, online teaching is entirely in a 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

### 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.
04.02 Special continuous distributions :  Gaussian distributions, Chi-squared, the t-distribution, the F-distribution.

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

06. Statistical Inference:
06.01 Random samples.
06.02 Consistent and unbiased estimators.
06.03 Sample mean and variance.
06.04 Normal samples.
06.05 Maximum Likelihood Estimation.

07.  Hypotheses testing:
07.01 Hypotheses testing for mean and variance of a normal sample.  Hypotheses testing for mean and variance of normal  independent samples.
07.02 Confidence intervals: confidence intervals for mean and variance of a normal sample.
07.03 Goodness of fit test.
07.04 Test of independence.

### 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

### Supporting Activities

The teaching material and specific communications from the lecturer can be found, together with other supporting activities, 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.

R. Lupini, "Lezioni di Probabilità e Statistica", Quattroventi.

W. Navidi, "Statistics", Mc Graw-Hill.

D. Posa e S. De Iaco: ”Fondamenti di statistica inferenziale”, CLEUP.

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

Assessment

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.

R. Lupini, "Lezioni di Probabilità e Statistica", Quattroventi.

W. Navidi, "Statistics", Mc Graw-Hill.

D. Posa e S. De Iaco: ”Fondamenti di statistica inferenziale”, CLEUP.

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

Assessment

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.

 « back Last update: 10/05/2017

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