PROBABILITY AND STATISTIC

The course is one of the quantitative training activities of the Bachelor's Degree Programmes in Engineering. The aim is to get the student familiar with the main statistical and probabilistic methods for engineering and the sciences.
The course provides knowledge of statistics and probability, as well as skills in the use of specific programs for probabilistic calculus, simulation and data analysis.
At the end of the course, the student will be able to identify suitable statistical and probabilistic models and methodologies in the context of interest.

1. Knowledge and understanding:
- to know the main descriptive tools for summary and graphical representation of statistical variables
- to know the basic concepts of elementary probability, probability distributions and limit theorems
- to know and understand the main methods of statistical inference

2. Ability to apply knowledge and understanding:
- to use specific theoretical knowledge for calculations with probability distributions
- to use appropriate formulas and terminology in all the processes of application and communication of the acquired knowledge

3. Ability to judge:
- to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods

4. Communication skills:
- to present in a clear and exhaustive way the results obtained from solving a statistical or probabilistic problem, using rigorous formulas and appropriate terminology

5. Learning skills:
- to use and merge information from notes, books, slides and practical lab sessions
- to assess the achieved knowledge through quizzes, exercises and assignments during the course

It is strongly suggested to attend CALCULUS I [CT0560].
This course requires good mathematical knowledge about: limits of functions, sequences and series, differential calculus of one real variable, integral calculus for functions of one real variable.

Descriptive statistics: Population, samples and variables; indexes of position, spread and correlation; graphical representations of statistical variables.
Probability: combinatorial analysis; sample space, events and probability; conditional probability and independence; discrete and continuous random variables; expectation and moments; joint distributions of random variables, covariance and correlation; functions of random variables; central limit theorem and law of large numbers; simulation and Monte Carlo methods.
Inference: parameters, estimators and sample distributions; confidence intervals and tests of significance; linear regression model.

Main textbook:
S.M. Ross (2023). Probabilità e statistica per l'ingegneria e le scienze. Quarta edizione. Apogeo.
S.M. Ross (2014). Introduction to Probability and Statistics for Engineers and Scientists. 5th ed. Academic Press.

Suggested books:
W. Navidi (2006). Probabilità e statistica per l'ingegneria e le scienze. McGraw-Hill
W. Navidi (2019). Statistics for Engineers and Scientists. 5th ed. McGraw-Hill.
R.E. Walpole, R.H. Myers, S.L. Myers (2020). Probabilità e statistica per ingegneria e scienze. Strumenti e applicazioni in R. Nona edizione. Pearson.

The achievement of the course objectives is assessed through participation in activities during the course and a written final exam.
Among the activities proposed during the classes there will be quizzes to assess understanding of basic concepts and exercises to be solved alone or in groups. Active participation in these activities is evaluated 4 points maximum.
The final exam (30 points) is composed by exercises similar to those solved or assigned during the course. During the written exam the use of notes, books and other teaching material is not allowed. A textbook will be available for consultation. An example of exam will be made available in Moodle.
A part of the written test may be replaced by an intermediate partial written test (the "first part") to be taken during the class period. The completion of the partial test (the "second part") may be held only during the first or second exam, as an alternative to these. After the delivery of the entire written test or after the delivery of the "second part", the "first part" loses its validity.
Regarding the grading scale (how grades will be assigned):
1. Scores in the range of 18-22 will be assigned when:
- adequate ability to use specific theoretical knowledge for calculations
- sufficient ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- limited ability to critically interpret the obtained results
- sufficient communication skills, using rigorous formulas and appropriate terminology
2. Scores in the range of 22-26 will be assigned when:
- good ability to use specific theoretical knowledge for calculations
- adequate ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- sufficient ability to critically interpret the obtained results
- adequate communication skills, using rigorous formulas and appropriate terminology
3. Scores in the range of 26-30 will be assigned when:
- excellent ability to use specific theoretical knowledge for calculations
- good or excellent ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- good ability to critically interpret the obtained results
- good or excellent communication skills, using rigorous formulas and appropriate terminology
4. Honors will be granted to students in the range 3. that have participated with commitment and interest to the activities during the course.

The main methodology used in this course is active learning, in which students are asked to participate in different activities by answering questions and solving exercises individually or in groups. Classical lessons only take a small part of the class, leaving to individual home study the knowledge of simple concepts.

Italian

written