Teaching code

4S02843

Credits

6

Coordinator

Matteo Calgaro

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 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.

Prerequisites and basic notions

A solid knowledge of basic mathematics is required. Specifically, the following are required:
- to be able to solve equations and inequalities (first and second degree);
- to understand the main real functions (linear, quadratic, exponential, logarithmic), their domain and behavior;
- to be able to work with sequences and limits;
- to understand the fundamentals of differential and integral calculus for functions of one real variable: derivatives, qualitative study of functions, definite integrals.
- to understand basic linear algebra: operations with vectors and matrices, solving linear systems, and the concept of matrix inverses.

Program

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UL: 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.
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UL: Laboratorio
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The course includes a series of laboratories with exercises in a scientific computing environment. Firstly, the scientific computing environment and the main functions and tools useful for statistics are introduced. Then, exercises in descriptive statistics, probability, calculation of the probability density function (pdf) and cumulative density function (cdf) for models of random variables, random data generation, parameter estimation, hypothesis testing for distributions, and linear regression will be proposed. Labs complement lessons by consolidating learning and developing practical problem-solving skills.

Bibliography

Didactic methods

Lectures and laboratory sessions with R.

Learning assessment procedures

The exam consists of a computer test via Moodle. The exam consists of theoretical questions (test with multiple choice) and problems. Some questions and exercises need to be solved with the help of the statistical software R.

Evaluation criteria

At the end of the course, the student must demonstrate knowledge and understanding of the main statistical and probabilistic techniques for the description and analysis of the phenomena under study; have the ability to apply the knowledge acquired and understanding to interpret the results of the statistical analyses applied in a critical and proactive manner, also through the tools shown; be able to develop the skills necessary to continue studies independently in the field of statistical analysis.

Criteria for the composition of the final grade

The score of the Laboratory part will be averaged with the score of the Theory part.

Exam language

Italiano/Inglese

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