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 (4 hours) • Univariate random variables (8 hours) • Conditional, marginal and joint distributions; conditional expectations (6 hours) • Important multidimensional distributions (multinormal, multinomial) (6 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 textbook Jay Devore. Probability and Statistics for Engineering and the Sciences. Any of various editions (Duxbury, Cengage, International). 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). Casella, George, and Roger L. Berger. Statistical inference. Any of various editions

Exam: Optional oral exam; Computer-based written test using the PoliTo platform;

STRUCTURE OF THE EXAM The structure of the exam does not change with respect to that of the previous yearbook. 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 with 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. Examples of quizzes and exercises are available in the materiale section of the portal. 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 is 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. ONLINE EXAM The written test will take place through the EXAM platform, integrated with proctoring tools (Respondus), which requires possession of a PC equipped with a camera. Students must follow the instructions provided by the University regarding the use of this platform. Students will give their answers to the multiple-choice questions (20 minutes) and to the exercises (90 minutes) through the EXAM platform. After 20+90 minutes each student will have 10 minutes to upload the file containing the scans of the solutions on portale della didattica, sezione elaborati. Students should create a single PDF containing all the scans. The optional oral exam will be carried on using a virtual classroom.

Exam: Written test; Optional oral exam; Computer-based written test using the PoliTo platform;

Both for online and onsite exams the rules are those described in the section "Assessment and grading criteria for online exam". More specifically for onsite exams, the rules are described in sub-section "STRUCTURE OF THE EXAM" while those for online exams the rules are described in sub-sections "STRUCTURE OF THE EXAM" and "ONLINE EXAM".