Introduction to statistics and data analysis. Introduction to probability. Random variables, parametric estimation, hypothesis testing, linear regression, logistic regression, analysis of variance
S. Ross. Introduction to Probability and Statistics for Engineers and Scientists. Academic Press; 4th edition (March 13, 2009)
Obiettivi Formativi
The aim of this course is to provide students with the foundamental methodological tools needed for statistcal design and data analysis for engeneering applications. The course will contribute to the following learning objectives specific of the Master Programme:
Knowledge and understanding
cc11 Knowledge of the tools for statistical data analysis and processing (descriptive and inferential) also by means of artificial intelligence.
cc13 Knowledge of the methods and tools for the development of a cooperative work activity.
Applying knowledge and understanding
ca6 The ability to manage complex and multidisciplinary projects and organizations and to make their development sustainable.
Making judgements
ag1: The ability to independently analyse data and information, draw objective conclusions and make consequential decisions.
Communication skills
ac1: The ability to communicate and transfer information, ideas, problems and solutions to specialists and non-specialists.
ac2: The ability to professionally present problems, solutions, analyses and results through written reports and verbal presentations.
Prerequisiti
Differential and integral calculus
Metodi Didattici
Theoretical and practical classes:
Mention is made of the special importance of the student's personal effort and the development of orderly study habits for a good learning process. An important methodological aspect is to stimulate student participation in the development of the theoretical and practical classes. Students will be asked questions, directly and also the use of student response systems. Practical classes will develop the application of knowledge and the ability to solve statistical problems.
Application workshop with peer-to-peer review:
As solving statistical problems is a key ability, it will be reinforced through an applicative workshop. The activity foresees the assignment of a problem to small groups, who are requested to analyze and solve it within a defined time frame. The discussion within the group will activate critical thinking and the ability of making judgments based on data.
Student study:
Review and reinforcement of theoretical concepts.
Modalità di verifica apprendimento
The level of knowledge acquired by the student is assessed by means of two intermediate tests, carried out during the course. Students who do not reach the minimum knowledge level (or who have not taken the two intermediate tests) must take a written test on the entire course program.
Each of these tests is comprised of several written exercises concerning statistics and probability and aims at verifying the knowledge and understanding of students of methods and tools proper of the discipine.
To pass the exam, students must demonstrate the ability to understand complex and multidisciplinary problems (ca6), formalize them from a statistical point of view, and efficiently apply statistical tools and methods presented during the course (cc11, cc13, ag1). Additionally, it must emerge the ability to professionally present and discuss results of the analysis in a comprehensive manner (ac1, ac2).
Programma del corso
Elements of probability: sample space and events, event algebra, axioms of probability, conditional probability.
Random variables: simple distributions, joint distributions and conditional distributions, expected value and variance of distributions of random variables, models for discrete random variables (Bernoulli, Binomial, Poisson, Hypergeometric), models for continuous random variables (Uniform, Normal, Exponential, Gamma , Weibull, distributions deriving from the Normal).
Sampling distributions and Central Limit Theorem.
Parametric estimation: maximum likelihood estimators, confidence intervals for the mean, proportion, variance and difference between means.
Hypothesis testing: test on mean, proportion, variance and difference between means.
Simple linear regression: parameter estimation and model verification. Logistic regression model. Analysis of variance (time permitting).