Unit PROBABILITY AND STATISTICS I

Course
Mathematics
Study-unit Code
A001545
Curriculum
In all curricula
Teacher
Andrea Capotorti
CFU
12
Course Regulation
Coorte 2020
Offered
2021/22
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa integrata

PROBABILITY ANS STATISTICS - I MODULE

Code A001546
CFU 6
Teacher Andrea Capotorti
Teachers
  • Andrea Capotorti
Hours
  • 47 ore - Andrea Capotorti
Learning activities Caratterizzante
Area Formazione modellistico-applicativa
Academic discipline MAT/06
Type of study-unit Obbligatorio (Required)
Language of instruction Italian
Contents Basic notions of descriptive statistic; linear regression, parametric estimation, confidence intervals, hypothesis testing.
Coherence principle.
Reference texts Main references:
Iacus S.M., Masarotto G.: Laboratorio di statistica con R. McGraw-Hill.
Erto P.: Probabilita' e Statistica per le scienze e l'ingegneria, Mc-Graw-Hill, ed. 2004
R. Scozzafava: Incertezza e Probabilità (Zanichelli).


Alternatively:
S. Ross, Introduction to probability and Statistics for Engineers and
Scientists, Academic Press, 2009.
Educational objectives Knowledge and ability on basic probability, descriptive and inferential statistical notions.Students will be able to face and solve practical and theoretical problems about descriptive statistic, linear regression and hypothesis tests. They will be also able to consciously express the learned notions.
Prerequisites Basic calculus notions, basic notion of Algebra and combinatorics. Basic computer abilty. To fully understand the subjects are recomended the know what is teached in the courses "Analisi Matematica I & II", "Informatica I"
Teaching methods Theoretical lessons on all the subjects and practical exercises developed also with the specific statistical software R
Other information For students with Specific Learning Disorders and/or Disabilities please refer to the we page: http://www.unipg.it/disabilita-e-dsa
Learning verification modality Practical exercises in R apt to check ability in solving practical basic statistical problems and oral examination apt to verify the consciuosness and ability in manipulation of the studied notions.
Exercises in R will be 5 or 6 based on real or simulated data. Each exercise will have a maximum degree (usually between 3 and 10, depending on the complexity required).
To pass to the oral test, a degree of at least 18/30 must be taken in pratical part in R.

On request, the exam can be done in English.
Extended program Descriptive statistics: statistical unitary, frequencies or in classes distributions; graphical representations; mean values: mode, median, arithmetic mean, means “a la Chisini”; means properties; variability indices; quantiles, Boxplots; double empirical distribution: joint, marginal, conditional frequencies, chi-squared dependence index.Liner regression: min-squared estimates; previsions; R2 index.
Principal probability distributions: binomial, geometric, Poisson, uniform, exponential, normal. Distributions of sample statistics: chi-squared and t-student.
Parametric estimation: main estimators and their properties.Interval estimation: general method; specific cases for the mean and variance of normal populations.Hypothesis testing: generic parametric tests and particular cases with normal populations; non parametric tests: binomial, adaptation an independence tests.

PROBABILITY AND STATISTICS - II MODULE

Code A001547
CFU 6
Teacher Alessandra Cretarola
Teachers
  • Alessandra Cretarola
Hours
  • 47 ore - Alessandra Cretarola
Learning activities Affine/integrativa
Area Attività formative affini o integrative
Academic discipline SECS-S/06
Type of study-unit Obbligatorio (Required)
Language of instruction Italian.
Contents Introduction to probability theory and its applications.
Reference texts P. Baldi, Calcolo delle Probabilità, McGraw-Hill, second edition, 2011.

Suggestion for further exercises:
F. Biagini, M. Campanino: Elementi di Probabilità e Statistica, Springer, 2006.

Alternatively:
S. Antonelli, G. Regoli: Probabilità discreta; esercizi con richiami di teoria, Liguori Ed., 2005.
Educational objectives This course is the first approach to probability theory.
The main aim of this teaching is to make students able to reason in a probabilistic framework and use probabilistic models for solving problems involving uncertainty.
Prerequisites Basic calculus notions, basic notion of Algebra and combinatorics. To fully understand the subjects, the contents provided in the courses Analisi Matematica I & II are recommended.
Teaching methods Lectures on all the topics of the program for 5 CFU (35 hours).
Proposal and resolution of problems relating to all program arguments for 1 CFU (12 hours).
Other information For students with Specific Learning Disorders and/or Disabilities please refer to the we page: http://www.unipg.it/disabilita-e-dsa.
Learning verification modality Examination divided into a preliminary written and a consequently oral examination.
- Written part, of about 2h mean duration, is composed of 3 exercises and is apt to verify problem solving skill and is about all the subjects;
- The oral examination can be done by students who will pass the written part with a mark of at least 18/30 or those who have passed intermediate similar tests ("esoneri") during the term. It is of 30 min in the average, and is apt to verify the presentation skill and the learning level.
On request, the exam can be done in English.
Extended program Theoretical aspects about: events, conditional probability, independence. The Bayes theorem. Random variables, probability distributions, density and distribution functions, discrete and continuous random variables and their properties. Expected value, variance, moments. Jointly distributed random variables: joint and marginal distributions, conditional distributions. Relations among random variables; transformations of random variables; joint probability distribution of functions of random variables.
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