AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide students the fundamentals in probability and inferential statistics, allowing them to build simple probabilistic models of interest in the applications and to acquire necessary techniques to answer predictive questions on said models, mostly through autonomous solving of exercises.

AIMS AND LEARNING OUTCOMES

The main learning outcomes are

• basic concepts of probability and descriptive statistics
• knowledge of the properties of the main probability distributions
• ability to construct probabilistic models to describe random phenomena
• knowledge of some statistical tests 
• ability to solve exercises, discussing the reasonableness of the results obtained

TEACHING METHODS

60 hours in a classroom with blackboard (40h theory and 20h excerices).

SYLLABUS/CONTENT

• Combinatorial calculus: fundamental principle of combinatorial calculus; arrangements, permutations and combinations; binomial coefficient and multinomial coefficients.
• Elements of probability: space of outcomes and events; axioms of probability; spaces of equiprobable outcomes; conditional probability; factorization of an event and Bayes formula; independent events.
• Random variables: discrete and continuous random variables; mass and density functions of probability; probability distribution function; ennuples 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 sum of random variables; generating function of moments; weak law of large numbers; change of variable; sum, difference, product and quotient of random variables. Mention of random vectors.
• Random variable models: Bernoulli and binomial random variables; Poisson random variables; hypergeometric random variables; uniform random variables; normal random variables; exponential random variables; Gamma random variables; chi-square random variables
• Descriptive statistics: populations and samples; sample mean, median and fashion; sample variance and standard deviation; sample percentiles; Chebyshev's inequality; bivariate data sets and sample correlation coefficient.
• Distributions of sample statistics: sample mean; central limit theorem; approximate distribution of sample mean; sample variance; sample mean and sample 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.

The lectures contribute to achieving the following goals of the UN Agenda 2030 for Sustainable Development
Goal 4: provide quality, equitable and inclusive education and learning opportunities for all
Goal 5: Achieve gender equality and empower all women and girls

RECOMMENDED READING/BIBLIOGRAPHY

S. M. Ross, Probabilità e Statistica per l'Ingegneria e le Scienze, Apogeo Milano (2003).

TEACHERS AND EXAM BOARD

Exam Board

ENRICO RIZZUTO (President)

ERNESTO DE VITO (President Substitute)

TOMASO GAGGERO (President Substitute)

DAMIANO POLETTI (President Substitute)

CESARE MARIO RIZZO (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8738/p/studenti-orario

EXAMS

EXAM DESCRIPTION

The exam is a two-hour  test and it connsists of solving three exercises
on the topics covered during the year . To participate in the written test, one must register by the deadline at

https://servizionline.unige.it/studenti/esami/prenotazione

ASSESSMENT METHODS

The written test aims to verify the ability of the student on computational techniques and on the knowledge of the main tools of probability and statistics (random variables, random vectors, random variable functions, limit theorems, estimators, hypothesis testing). The exams consists of three exercises divided into several questions of different difficulty.   The student must be able to solve the exercises correctly and be able to justify the steps necessary to obtain the final result and use the correct formalism. 
The duration of the test is 2 hours. It is possible to consult notes, textbooks and use the scientific calculator.

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

Exam schedule