## PROBABILITY AND STATISTICS PROBABILITÀ E STATISTICA MATEMATICA

A.Y. Credits
2022/2023 6
Lecturer Email Office hours for students
Alessia Elisabetta Kogoj Wednesday and Thursday 13:00-14:00 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, 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 (strongly 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

Eventual teaching material made available by the lecturer can be found, together with other supporting activities, inside the Moodle platform › blended.uniurb.it

### Didactics, Attendance, Course Books and Assessment

Didactics

Theory lectures and exercises.

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 knowledge, understanding and ability to communicate are assessed with a written exam with open questions. After having passed the written exam students can attempt an oral examination.

### Additional Information for Non-Attending Students

Didactics

Theory lectures and exercises.

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 knowledge, understanding and ability to communicate are assessed with a written exam with open questions. After having passed the written exam students can attempt an oral examination.

### Notes

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

 « back Last update: 19/07/2022

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