PROBABILITY CALCULUS AND STATISTICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2015/2016
- Teacher
- ANGELA GRASSI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- MAT/06
Training objectives
- The aim of the course is to teach the basic concepts of statistics and probability and their application to data analysis and to the study of random phenomena.
In particular, the main knowledge acquired by students include: techniques of descriptive statistics, basic elements of probability theory and statistical inference methods.
Students will also gain the ability to set up and properly solve probabilistic and statistical problems, using as appropriate the techniques learned. Prerequisites
- Basic notions of mathematics are essential. Notions of differential and integral calculus, learned during the course of Principles of Mathematics which is held in parallel, are very useful.
Course programme
- The course includes 48 hours of lectures divided between theory and exercises. On the course website is published the detailed schedule of classes, where for each date is specified the topic addressed and if the lesson is theory or exercises.
Topics covered in the course are the following.
1. Descriptive statistics (12 hours): frequency distribution, representation and synthesis of data through graphs and tables, measures of central tendency and of variability, correlation.
2. Probability theory (12 hours): basic concepts, conditional probability and independence of events, Bayes theorem, main discrete distributions and Normal distribution, Central Limit Theorem.
3. Statistical inference (16 hours): sampling distributions, point estimation, interval estimation, hypothesis testing.
4. Simple linear regression (8 hours): specification and estimation of the model, predictions based on the model, computing the sum of squares, coefficient of determination, standard error of the estimates. Didactic methods
- The course includes theoretical and practical lectures on all topics. Practical lectures are organized as blackboard sessions in which the lecturer proposes and solves exercises designed to illustrate the use of the techniques learned during the course.
Learning assessment procedures
- Written examination that aims to assess the level of preparation of students through exercises and theoretical questions on the topics covered in the course. The examination is structured as a multiple choice test composed of 17 questions. For each question there are three possible answers, of which only one exact. The score assigned is: +2 for each correct answer, -1 for each wrong answer, and 0 for each question not answered. To obtain full score in a question (+2), both the answer and the procedure carried out by the student to get to the answer must be correct. The final grade is the sum of the scores of the individual questions. To pass the exam it is necessary to obtain a minimum of 18 out of 34. The maximum grade (30 e lode) is assigned in the case of sum of scores greater than 30. The exam duration is 90 minutes. The consultation of texts or notes is not permitted.
Reference texts
- D.M. Levine, T.C. Krehbiel, M.L. Berenson, "Statistica", V edizione, Pearson, Milano, 2014.
S. Bonnini, A. Grassi, "Esercizi svolti di statistica e calcolo delle probabilità", Volta la carta, Ferrara, 2015.
Additional material and information is available on the website of the course.
