The teaching is organized as follows:

Learning objectives

The course aims to provide the basic concepts of descriptive statistics and probability calculus, focusing on the application of these concepts to the engineering context. The goal is to provide the student with the necessary tools to model and solve concrete problems through the use of probabilistic methods and to apply the main statistical techniques to engineering for the analysis of real problems. At the end of the course the student will have to demonstrate knowledge and understanding of the main statistical techniques for the description and analysis of the phenomena under study; have the ability to apply the acquired knowledge and understanding to interpret the results of the statistical analyzes applied in a critical and proactive way, also through the tools shown; knowing how to develop the skills necessary to continue their studies independently in the field of statistical analysis.

Program

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MM: Teoria
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(1) Descriptive Statistics. Describing data sets (frequency tables and graphs). Summarizing data sets (sample mean, median, and mode, sample variance and standard deviation, percentiles and box plots). Normal data sets. Sample correlation coefficient. (2) Probability theory. Elements of probability: sample space and events, Venn diagrams and the algebra of events, axioms of probability, sample spaces having equally likely outcomes, conditional probability, Bayes’ formula, independent events. Random variables and expectation: types of random variables, expected value and properties, variance, covariance and variance of sums of random variables. Moment generating functions. Weak law of large numbers. Special random variables: special random variables and distributions arising from the normal (chi-square, t, F). (3) Statistical inference. Distributions of sampling statistics. Parameter estimation (maximum likelihood estimators, interval estimates). Hypothesis testing and significance levels. (4) Regression. Least squares estimators of the regression parameters. Distribution of the estimators. Statistical inferences about the regression parameters. The coefficient of determination and the sample correlation coefficient. Analysis of residuals: assessing the model. Transforming to linearity. Weighted least squares.
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MM: Laboratorio
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The course includes a series of laboratories in the computer lab with exercises in MATLAB environment. After an introduction to MATLAB and to the main functions and tools useful for statistics, some exercises will be proposed on descriptive statistics and probability; for computing the probability density function (pdf) and cumulative distribution function (cdf) of special random variables, for generating random data and estimating parameters; on hypothesis testing for distributions and linear regression. The laboratories complement lectures by consolidating learning and developing problem-solving and hands-on practical skills.

Learning assessment procedures

The exam consists of a computer test via Moodle. The exam consists of theoretical questions (test with multiple choice), problems, and laboratory questions (open questions).