Probability and Statistics (2021/2022)
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
The teaching is organized as follows:
The course aims at providing the fundamental concepts of descriptive statistics and probability, with the task of modeling real problems by means of probability methods and applying to real problems statistic techniques. At the end of the course the student will have to demonstrate to understand the main statistical techniques for describing problems; to be able to interpret results of statistical analyses; to be able to develop know-how necessary to continue the study autonomously in the context of statistical analysis.
(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.
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. Teaching 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.
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.
Written exam consisting of theoretical questions (test with multiple choice), problems, and laboratory questions (open questions). 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.