PROBABILITY CALCULUS AND STATISTICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2021/2022
- Teacher
- STEFANIA BARTOLETTI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- ING-INF/03
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
- 1. Descriptive statistics: frequency distribution, representation and synthesis of data through graphs and tables, measures of central tendency and of variability, correlation.
2. Probability theory: basic concepts, conditional probability and independence of events, Bayes theorem, main discrete distributions and Normal distribution, Central Limit Theorem.
3. Statistical inference: sampling distributions, point estimation, interval estimation, hypothesis testing.
4. Simple linear regression: 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 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. 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.
As a further teaching support, a 8 hour computer lab activity is scheduled where the lecturer will introduce to programming in the R statistical environment, with practical applications of the concepts learned in class. Learning assessment procedures
- Oral examination that aims to assess the level of preparation of students through an exercise to be discussed (from 0 to 14), the solution of part of the exercise on R (from 0 to 4), and theoretical questions (from 0 to 14).
Reference texts
- Lecture notes
Suggested:
S. M. Ross, Probabilità e statistica per l'ingegneria e le scienze
Additional resources for further study.
G. Casella, R. L. Berger, Statistical Inference
Dimitri P. Bertsekas, John N. Tsitsiklis, Introduction to Probability, 2nd Edition
Hogg, Tanis, Zimmerman, Probability and Statistical Inference, 9th Edition
