Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Elementary algebra. Differential and integral calculus of the functions of one and more variables.

The aim of the course is that of providing the theoretical, methodological and practical elements of probability theory and statistics. The objective is that of solving typical problems of engineering management and of industrial engineering, including problems of high complexity, incomplete definition or contradicting characteristics. Also important is the acquisition of knowledge about analyzing and solving problems related to new and emerging areas of businness management. In particular, the course aims at providing the student with the basic elements of probability distributions and of some standard problems of statistics, suche as parameter estimation and hypothesis testing.

In order to develop the students ability to use statistical methods towards the formulation of models, the analysis and the solution of problems, the main classical results of probability and statistics will be introduced, accompanied by numerous applications. This path will lead the student to achieving the capability of using the elements of probability theory and the tools of descriptive and inferential statistics, in order to model quantitatively the problems and to generate decision support systems.

Individual and collective problem-solving sessions, aimed at detecting, formulating and solving engineering management problems, will improve the ability to develop independent thought and learning capabilities. Oral presentations of the main topics introduced in the course will help developing communication skills.

1. Probability spaces. 2. Discrete random variables. 3. Continuous random variables. 4. Convergence and approximation: law of large numbers and central limit theory. 5. Mathematical statistics: estimates, sampling, regression, hypothesis tests.

The exam consists of a written test and a colloquium: - both tests will concern the topics of the current academic year; possible exceptions will be assessed on a case-by-case basis; - registration to the first written test is mandatory, and has to be done on line on the university platform Esse3 (the link is available on the teacher's web page); - the written test consists of a number of problems and questions concerning all topics treated during the course; this test will last two or three hours, and the student will not be permitted the use of any kind of material, but for a pocket calculator; - a minimum score of at least 18/30 in the written test is required for the admission to the oral test; - the list of the names of the students admitted to the oral test will be published by the teacher on his official web page; - the oral test will contain mainly theoretical questions, some of which may have to be formulated in written form, and may contain problems and exercises concerning course topics not covered in the written test or course topics in which the student may have shown weaknesses in the written test; - questions of general comprehension may be asked both in the written and in the oral test and may concern any of the course topics; - in the case of a successful written test, the student may sit for the oral test either in the same session or in the next available session, but not later; - in the case of a successful written test, but a not passing grade in the oral test, the student may try the oral test again in the next available session; in case of another failure, the student will have to sit for the whole exam again; - all written tests must be presented in readable form, with a negligible amount of corrections, which must anyway not mar the esthetics of the text; the exposition must be clear, fluent, well organized and consistent both in the mathematical and in the linguistic aspects; - honor code: each student pledges that the written tests are entirely his/her own work and that no input from other students or sources has been used; demeanors which are deemed unfair or not in line with these principles entail the failing of the exam.

In order to pass the exam, the student must demonstrate understanding of all the topics covered and concepts introduced during the course and published on line as "Final program" or "Exam program" at the end of the course, and to be able to use them in solving typical problems of probability and statistics.

The student must demonstrate to have acquired deep knowledge on the fundamental principles and techniques of probability and statistics and on the solution of typical problems arising within the topics covered during the course.

The highest grade of 30/30 will be given to those students which will have shown deep knowledge and perfect mastering of all the course topics and the ability of working with full independence both in solving the assigned problems and in the oral presentation. The lowest passing grade of 18/30 will be given to the students which will have shown sufficient knowledge and good mastering of all the course topics.

Sheldon M. Ross, "Probabilità e statistica per l'ingegneria e le scienze" (a cura di F. Morandin), Apogeo 2008; T. T. Soong, Fundamentals of Probability and Statistics for Engineers, Wiley 2004

- Ingegneria Gestionale (Corso di Laurea Magistrale Fuori Sede (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

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