Basic concepts in Probability and Statistics will be presented to students coming from backgrounds different from Mathematics or Statistics.

The student will learn the basics of Statistics (sampling distributions, estimates, test statistics, p-values, confidence intervals), solidly based on Probability theory. The aim is for the student to be able to model uncertainty in the real world, to draw conclusions from the accrual of evidence and to formulate them in probabilistic terms using appropriate software.

Extensive knowledge of calculus, basic knowledge of combinatorics and discrete probability.

• Review of elementary probability theory and univariate random variables (8 hours) • Conditional, marginal and joint distributions; conditional expectations (6 hours) • Important multidimensional distributions (multinormal, multinomial, DAGs) (10 hours) • Convergence of probability laws and limit theorems (8 hours) • Sampling distributions and point estimation (12 hours) • Confidence intervals with applications to basic designs (11 hours) • Hypothesis testing, including goodness of fit (e.g. chi-square) (11hours) • Software for statistical analysis (14 hours)

Traditional classes, exercise sessions and computer based sessions will be intertwined. The student will learn software by doing and by making the most out of extensive support given in the web.

Reference textbooks Jay Devore. Probability and Statistics for Engineering and the Sciences. Any of various editions (Duxbury, Cengage, International). Casella, George, and Roger L. Berger. Statistical inference. Any of various editions Further readings Ross, S. Introduction to Probability and Statistics for Engineers and Scientists. Anyone of various recent editions (Italian translation by Apogeo). Ross, S. A first course in probability. for Engineers and Scientists. Anyone of various recent editions (Italian translation by Apogeo). Robert I. Kabacoff. R in action. Manning. 2nd edition 2015.

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The exam consists of a written examination and an optional oral examination. Both the written and the optional oral part of the exam concerns all the subjects dealt during the course. The aim is to test the student's ability to apply the methods of analysis described during the course and to understand the software tools, without much emphasis on mathematical proofs. The duration of the written exam is two hours. The written exam is made by two parts: 8 quizzes (multiple choice questions) and 4 exercises. The maximum time for the 8 quizzes is 20 minutes. With respect to the 8 quizzes the score for each correct answer is 1 point, 0 points for each wrong or not given answer. The maximum score for the part made by the 8 quizzes is 8/30 points. In this part of the written exam textbooks, student notes or formularies are not allowed. The use of non-programmable electronic calculators is allowed. The maximum score for the part made by the 4 exercises is 24/30 points. In this part of the written exam textbooks, student notes or formularies provided by the teacher during the year are allowed. The use of non-programmable electronic calculators is allowed. The total score obtained in the written test is the sum of the one obtained in the quizzes (max 8/30) and that obtained in the part of exercises (max 24/30). If the total score is 31/30 or 32/30 then the exam score is "30 e lode". To pass the written exam at least 4/30 points in the quizzes and at least 18/30 as total score are required. The oral exam is possible under request for those students that in the written exam get a positive mark (i.e. at least 4/30 points in the quizzes and at least 18/30 as total score). Following the oral test, the mark obtained in the written part of the exam can be increased or decreased by no more than 6 points. During the oral exam the student will have to demonstrate knowledge of the concepts and of the results seen in class. The student will have to be able to provide examples and to solve simple exercises which may be asked by the teacher.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.