Ateneo - UPO

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes formula.
Discrete and continuous random variables, independent random variables, expected values. Variance and covariance.
Special random variables: Bernoulli and binomial random variables, hypergeometric and geometric variables. Poisson distribution,
uniform random variables, normal random variables, exponential random variables. Central Limit Theorem. Basic statistics. Set of data,
mean, quartiles. Definition of sample statistics, sample variance. Parameter estimations. Hypothesis testing and applications.

Sheldon M. Ross: Introduction to probability and statistics for Engineers and scientists, Elsevier 2004 (Probabilità e Statistica per l'Ingegneria e le Scienze,Apogeo Education – Seconda Edizione 2008)

To provide students with the fundamental skills in probability theory and inferential statistics, necessary for formal modeling and quantitative data analysis in computer science, consistent with the educational objectives of the program. Upon completion of the course, students will be able to:
-Formalize uncertain problems using probabilistic models and random variables (discrete and continuous).
-Calculate sample statistical parameters, apply the main limit theorems, and perform parametric estimates and hypothesis tests on real data sets.

Basic notions of the courses of Mathematical Analysis I and Discrete Mathematics.

Class lectures with exercises.
During the exercises, the Professor encourages active participation from students, guiding them through the exercises and discussing the various steps required to reach the solution.

The exam consists of a written test composed of several exercises and one or more theoretical questions on the theoretical part. Students who pass the written part (with at least 18) can request an oral exam (optional). Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The examination consists of a written test and an optional oral examination.

Structure of the assessments and Learning Outcomes assessed:
Written Test: 3–4 exercises and 1–2 theoretical questions. It assesses Knowledge and Understanding and the ability to Apply Knowledge and Understanding in probability and statistics, as well as Making Judgments in selecting an appropriate solution strategy.

Oral Examination:
-Optional: Available upon request by students who have passed the written test with a score of at least 18/30, in order to improve their grade.
-Mandatory / Upon invitation: The Professor reserves the right to directly invite a student to take an oral examination if deemed necessary to ascertain and verify the authenticity and authorship of the written work.

The oral examination consists of a discussion of the written work and theoretical questions aimed at assessing Communication Skills, formal rigor, and depth of understanding.

Assessment criteria and score ranges:
18–21/30 (Pass): Basic knowledge of the theoretical concepts; essential ability to apply formulas and perform calculations in standard exercises, despite some formal uncertainty.

22–26/30 (Fair/Good): Good knowledge of the subject; correct and independent solution of exercises; clear and appropriate presentation of theoretical and practical steps.

27–30/30 (Very Good/Excellent): Full theoretical and methodological mastery; flawless performance in application-oriented exercises; strong critical reasoning skills and formal rigor in the presentation.

30 cum laude: Outstanding excellence, complete autonomy in problem solving, and exceptional clarity and effectiveness in both written and oral presentation.

Basic probability theory: the axioms of probability, Venn diagrams, space with equally likely outcomes, conditional probability, Bayes formula.
Discrete and continuous random variables, independent random variables, expected values. Variance and covariance.
Special random variables: Bernoulli and binomial random variables, hypergeometric and geometric variables. Poisson distribution,
uniform random variables, normal random variables, exponential random variables.
Central Limit Theorem. Basic statistics. Set of data, mean, quartiles. Definition of sample statistics, sample variance. Parameter estimations, Maximal Likelihodd technique for common distributions. Confidence level and intervals. Hypothesis testing and applications.

Knowledge and Understanding: Acquire a solid mastery of the fundamental theoretical concepts of probability theory and descriptive and inferential statistics.
Applying Knowledge and Understanding: Be able to formalize and solve application-oriented problems in the field of computer science by modeling them using appropriate random variables; be able to perform parameter estimation and hypothesis testing for data processing.
Making Judgments (Transferable Skills): Be able to independently and critically select the most appropriate probabilistic model or statistical tool for the analysis and interpretation of specific types of computer science data.
Communication Skills (Transferable Skills): Be able to present and describe analytical procedures and the results of probabilistic and statistical analyses with formal rigor and appropriate mathematical language.
Learning Skills (Transferable Skills): Develop the methodological skills necessary to independently explore advanced topics in data science, machine learning, and stochastic analysis covered in subsequent studies.