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
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.
Lectures and frontal exercises, exercise sheets, guided exercises, in itinere self-assessment tests.
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
Ricevimento: Send a message to ernesto.devito@unige.it
MATTEO LODI (President)
MARCO STORACE
ERNESTO DE VITO (President Substitute)
ALBERTO OLIVERI (President Substitute)
https://corsi.unige.it/en/corsi/10716/studenti-orario
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.
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.
