Teaching code

4S00021

Credits

6

Coordinator

Silvia Francesca Storti

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Courses Single

Authorized

Moodle Seminars 0

The teaching is organized as follows:

Learning objectives

The course aims to provide the basic concepts of descriptive Statistics and Probability, by modeling concrete problems through the use of probabilistic methods and, at the same time, to underline the natural application of these concepts to mathematical Statistics. The course also aims to provide ac-tual tools to apply the main statistical techniques to real cases. By the end of the course, students will have to show their knowledge and understanding of the main statistical techniques for the description and analysis of the phenomena under study; to express the ability to apply the acquired knowledge and understanding skills for the interpretation of the results of the applied statistical analyses in a critical and proactive way, by using the available tools; to be able to employ the knowledge acquired to continue the studies independently in the field of statistical analysis.

Prerequisites and basic notions

-

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.

Bibliography

Didactic methods

Regular lectures with power point presentation and blackboard and laboratory exercises. Educational material will be available to students enrolled in the course on the Moodle platform. This material includes lecture presentations in PDF format and material related to laboratory activities. For further details and supplementary materials, please refer to the reference books.

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).

Evaluation criteria

To pass the exam, the students must show that: - they have understood the basic concepts of probability theory and statistics; - they are able to use the knowledge acquired during the course to solve the assigned problem; - they are able to program in MATLAB environment in the statistical and probabilistic context.

Criteria for the composition of the final grade

The final grade will be the average of the three grades (theory, exercises, laboratory). To pass the exam, a minimum score of 18 out of 33 is required. Distinction is awarded for scores above 30.

Exam language

Italiano