CODE  56841 

ACADEMIC YEAR  2021/2022 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/07 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  1° Semester 
MODULES  This unit is a module of: 
TEACHING MATERIALS  AULAWEB 
The course aims to illustrate to students the general aspects of statistics and probability theory with applications to the theory of stochastic processes.
Online lectures according to the schedule of the Master Degree.
Descriptive statistics: populations and samples; sample mean, median and mode; Sample variance and standard deviation; sample percentiles; Chebyshev inequality; bivariate data sets and sample correlation coefficient.
Combinatorics: fundamental principle of combinatorics; arrangements, permutations and combinations; binomial coefficient and multinomial coefficients.
Elements of probability: space of outcomes and events; axioms of probability; spaces of equally likely outcomes; conditional probability; factoring of an event and Bayes formula; independent events.
Random variables: discrete and continuous random variables; mass and probability density functions; probability distribution function; tuples of random variables; joint distribution for discrete random variables; joint distribution for continuous random variables; independent random variables; expected value and its properties; variance and its properties; covariance and variance of the sum of random variables; moment generating function; weak law of large numbers; change of variable; sum, difference, product and quotient of random variables.
Models of random variables: Bernoulli and binomial random variables; Poisson's random variables; hypergeometric random variables; uniform random variables; normal random variables; exponential random variables; Gammatype random variables; chisquare random variable; random variables of type t; Ftype random variables.
Distributions of sample statistics: sample mean; central limit theorem; approximate distribution of the sample mean; sample variance; sample mean and variance of normal populations; sampling from finite sets.
Parametric estimation: maximum likelihood estimators; maximum likelihood estimator for Bernoulli variables; maximum likelihood estimator for Poisson variables; maximum likelihood estimator for normal variables; maximum likelihood estimator for uniform variables; bilateral and unilateral confidence intervals; confidence intervals for the expected value of normal distributions of known variance; confidence intervals for the expected value of distributions of unknown variance; confidence intervals for the variance of normal distributions; approximate confidence intervals for the mean of a Bernoulli distribution; confidence intervals for the mean of an exponential distribution.
Inputoutput systems: inputoutput systems; linear inputoutput systems; time invariant inputoutput systems; linear and time invariant inputoutput systems; convolution of functions and its properties; general notions on the Fourier transform and its properties; hints on distributions and generalized functions; frequency response of LTI I / O systems.
Stochastic processes and their spectral characteristics: stochastic process; expected value, variance and autocorrelation function of a stochastic process; crosscorrelation function of two stochastic processes; stationary stochastic processes (in a weak sense); jointly stationary stochastic processes; ergodic stochastic processes; power spectrum of a stationary stochastic process and its properties; cross power spectrum of two jointly stationary stochastic processes; response of inputoutput systems to stochastic processes; stochastic Gaussian processes; stochastic Poisson processes.
Lecture notes.
S. Ross Introduction to Probability and Statistics for Engineers and Scientists
Office hours: Friday 1416
ENRICO RIZZUTO (President)
ERNESTO DE VITO (President Substitute)
TOMASO GAGGERO (President Substitute)
CESARE MARIO RIZZO (President Substitute)
All class schedules are posted on the EasyAcademy portal.
The exam is written and online until the end of the COVID19 emergency. Further information about the examination will be provided on AulaWeb.
The written examination verifies that the student has acquired and knows how to use the basic tools of probability theory (random variables, random vectors, functions of random variables, limit theorems) and statistics (estimators, hypothesis testing)
Date  Time  Location  Type  Notes 

14/01/2022  09:00  GENOVA  Scritto  
09/02/2022  09:00  GENOVA  Scritto  
10/06/2022  09:00  GENOVA  Scritto  
13/07/2022  09:00  GENOVA  Scritto  
14/09/2022  09:00  GENOVA  Scritto 