( english version )

Statistics ( 5 CFU ) Finalità

This course presents the basics of probability theory and discusses some standard statistical inference techniques that are commonly applied in management and production.

Programma

Probability spaces, conditioning, independence, total probabilities and Bayes formulae.

Continuous and discrete random variables, distribution functions (cumulative, density, mass), joint distributions, linear and nonlinear transformations. Expected value, variance. Sum, min and max of i.i.d. random variables.

Common types of random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, exponential, Gaussian, chi-square, gamma, t-Student and Fisher).

Convergence in probability, Law of Large Numbers, Central Limit Theorem, continuity correction.

Populations and samples, descriptive statistics, estimators (bias and consistency), sample mean and sample variance.

Parametric confidence intervals (Gaussian, Bernoulli and exponential populations).

Nonbayesian parametric tests, bi- and unilateral (same populations as above), tests for comparing two populations parameters (Gaussian and Bernoulli).

Continuous and discrete random variables, distribution functions (cumulative, density, mass), joint distributions, linear and nonlinear transformations. Expected value, variance. Sum, min and max of i.i.d. random variables.

Common types of random variables (Bernoulli, binomial, Poisson, hypergeometric, uniform, exponential, Gaussian, chi-square, gamma, t-Student and Fisher).

Convergence in probability, Law of Large Numbers, Central Limit Theorem, continuity correction.

Populations and samples, descriptive statistics, estimators (bias and consistency), sample mean and sample variance.

Parametric confidence intervals (Gaussian, Bernoulli and exponential populations).

Nonbayesian parametric tests, bi- and unilateral (same populations as above), tests for comparing two populations parameters (Gaussian and Bernoulli).

Attività d'esercitazione

Resolution of problems and excercises.

Modalità d'esame

Written test (on exercises only). One can ask for an optional oral examination (on both exercises and theory).

Propedeuticità

Analisi AB.

Testi consigliati

S. Ross - Probabilitą e statistica per l'ingegneria e le scienze - Apogeo. (Also available in English.)