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CODE 97167
ACADEMIC YEAR 2024/2025
CREDITS
SCIENTIFIC DISCIPLINARY SECTOR MAT/06
LANGUAGE Italian
TEACHING LOCATION
  • GENOVA
SEMESTER 2° Semester
MODULES Questo insegnamento è un modulo di:
TEACHING MATERIALS AULAWEB

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides knowledge to understand the basic definitions of statistics and probability, to understand the difference between a deterministic and statistical approach, to understand the notion of a random variable and to be able to use probability to pass from descriptive statistics to analysis. data through inferential statistics. The student acquires knowldge to build simple statistical-probabilistic models (possibly adapting classical schemes) and discuss the results given by the models

AIMS AND LEARNING OUTCOMES

The expected learning outcomes require the student to be able to handle the basic definitions of statistics and probability, to understand the difference between a deterministic and statistical approach, to have acquired the notion of a random variable and to be able to use probability to pass from descriptive statistics to analysis. data through inferential statistics. The student must be able to build simple statistical-probabilistic models (possibly adapting classical schemes) and discuss the results given by the models.


 

TEACHING METHODS

Lectures and frontal exercises, exercise sheets, guided exercises, in itinere self-assessment tests.

 

 

SYLLABUS/CONTENT

Probability Definitions classical, a posteriori, axiomatic; conditional probability, independence; Bayes theorem, factorization theorem, law of total probability. Discrete and continuous random variables, distribution and density functions, function of random variable. Expected values, moments and theoretical variances. Joint distributions and conditional laws, covariance and correlation.

Descriptive Statistics Qualitative variables: categorical, ordinal; univariate descriptive: percentages and tables, bar and pie charts, Pareto chart, fashion; bivariate descriptive: row and column profiles. Quantitative variables: position indices (mode, median, mean, percentiles and quartiles), cumulative empirical distributions, boxplot; dispersion indices: range, IQR, variances and standard deviation, coefficient of variation; relationship between two quantitative variables: covariance and correlation, Simpson's paradox; linear regression, regression line, R2 coefficient and residual analysis.

Estimates and estimators. Principles of randomness, distortion, mean square error, efficiency.

Confidence intervals By mean (known / unknown variance, small and large sample sizes), by variance, by the difference of means (independent samples and paired samples). Funnel plot (weather permitting).

Statistical hypothesis tests Introduction, type I and II errors, p-value, level of significance, power. Test for the difference of means: independent samples and paired samples. Test for variance. Chi-squared test for categorical variables (comparison between a known distribution and an observed univariate, comparison between two observed univariate). ANOVA

RECOMMENDED READING/BIBLIOGRAPHY

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination consists of a written test lasting two hours and consists of solving three/four exercises
on the topics covered during the year . To participate in the written test, you must register by the deadline at https://servizionline.unige.it/studenti/esami/prenotazione.

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with the professor in charge of the Department’s disability liaison.

 

ASSESSMENT METHODS

The written test is aimed at verifying the student's mastery of calculation techniques and knowledge of the main tools of probability and statistics introduced in the course (random variables, random vectors, functions of random variables, limit theorems, estimators, hypothesis testing) and consists of three exercises consisting of several questions of varying difficulty.   The student must be able to correctly solve the exercises and be able to justify the steps required to obtain the final result and use the correct formalism.

Agenda 2030 - Sustainable Development Goals

Agenda 2030 - Sustainable Development Goals
Quality education
Quality education
Gender equality
Gender equality
Decent work and economic growth
Decent work and economic growth