corso|33498

Combinatorial analysis: Fundamental principle of combinatorics, mutations, combinations, multinomial coefficients Axioms of probability: sample space and events, equiprobable outcomes, probability as a continuous ensemble function, probability as a measure of confidence; conditional probability, Bayes formula, independent events Discrete random variables; the Binomial, Poisson, geometric, hypergeometric and negative binomial variables Continuous random variables; the uniform, normal and exponential variables (notes on the Gamma variable) Expected value and variance of discrete and continuous v.a. (and their properties) and of functions of v.a. joint laws of v.a., independent v.a., conditional distributions in discrete and continuous cases; covariance of two random variables and correlation coefficient Markov inequality and Chebyshev inequality; central limit theorem and weak law of large numbers (notes on the strong law of large numbers) Statistics; sample mean, median, mode and variance; maximum likelihood estimators; confidence intervals for the mean

A good knowledge, both conceptual and operational, of the contents of the Mathematical Analysis and Geometry course is required, in particular: limits of sequences, functions of a real variable, derivatives of the functions of a real variable and their applications, calculation of integrals , determinant of a square matrix.

Combinatorial analysis: Fundamental principle of combinatorics, mutations, combinations, multinomial coefficients Axioms of probability: sample space and events, equiprobable outcomes, probability as a continuous ensemble function, probability as a measure of confidence; conditional probability, Bayes formula, independent events Discrete random variables; the Binomial, Poisson, geometric, hypergeometric and negative binomial variables Continuous random variables; the uniform, normal and exponential variables (notes on the Gamma variable) Expected value and variance of discrete and continuous v.a. (and their properties) and of functions of v.a. joint laws of v.a., independent v.a., conditional distributions in discrete and continuous cases; covariance of two random variables and correlation coefficient Markov inequality and Chebyshev inequality; central limit theorem and weak law of large numbers (notes on the strong law of large numbers) Statistics; sample mean, median, mode and variance; maximum likelihood estimators; confidence intervals for the mean

A good knowledge, both conceptual and operational, of the contents of the Mathematical Analysis and Geometry course is required, in particular: limits of sequences, functions of a real variable, derivatives of the functions of a real variable and their applications, calculation of integrals , determinant of a square matrix.