MATHEMATICAL AND STATISTICAL METHODS FOR ENGINEERING
- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Delivery method
- Teaching methods
Knowledge of the topics covered in the courses of mathematical analysis, in particular series, differential and integral calculus for functions of a variable is required.
The final exam consists of conducting a data analysis and writing a report on the results obtained. The final dissertation has to be carried out individually. The final grade will be based on: in class participation (3 points maximum); originality; correctness; comments on the statistical analysis (both discrete and inferential).
The general objective of the course is to provide students with an introduction to probability theory, descriptive and inferential statistics. The second training objective is more applied and refers to the understanding of the context in which the introduction of probabilistic concepts and random variables is needed and, based on this understanding, it is required to know how to use the most suitable probabilistic / statistical tool and the best random variable to describe the engineering phenomenon of interest. Everything will be made more practical thanks to the introduction of the statistical software R that can be downloaded free of charge from the Internet through the website:
https://www.r-project.org
This software will allow students to describe and analyze data collected by them or others, summarizing them both in graphical and numerical form. Students will also know how to generalize these results from the sample to the entire population, ie to do what we call "statistical inference".
The course aims to
1) understand how random engineering-type phenomena can be modeled from a mathematical point of view through the concepts of probability and random variable;
2) define the main characteristics of random variables as the cumulative distribution function, the discrete and continuous density function and moments, making students familiar with their calculation;
3) introduce the main probability distributions of both discrete and continuous;
4) introduce the most important results on the convergence of random variables, such as the law of large numbers and the central limit theorem, and have students understand the importance of the latter in the solution of theoretical and applied problems;
5) introduce the main descriptive measures of a data set. Measurements of position and variability;
6) introduction to the statistical software R that students will be asked to install on their computer;
7) introduce the main tools to visualize a set of data and to summarize and synthesize a set of data using R;
8) introduction to hypothesis testing and linear regression.
At the end of the course students are expected to:
1) are able to formalize problems of probability calculation both in theoretical and applied contexts;
2) have acquired the necessary methodologies to calculate probabilities, expected values, variance and moments of both discrete and continuous random variables;
3) know the main cases of discrete and continuous random variables and know in which context to apply them;
4) are able to apply the results on the convergence of random variables for the solution of theoretical and practical problems;
5) know how to do basic statistical inference and linear regression,
On the e-learning website there will be the slides, the R commands done in class, and references on data used for the examples and for the final thesis.
The text book is
Statistica.
di Levine David M. - Szabat Kathryn A. - Stephan David F. - Arbia Giuseppe - Reinhold Jost - Ragozini
Giancarlo
Editore: Pearson
Anno: 2018
ISBN: 9788891902627
The book is also available in english.
Lectures with exercises done in the classroom. Students will be asked to bring their computer into the classroom.