Unit PROBABILITY AND STATISTICS I
- Course
- Mathematics
- Study-unit Code
- A001545
- Curriculum
- In all curricula
- Teacher
- Andrea Capotorti
- CFU
- 12
- Course Regulation
- Coorte 2024
- Offered
- 2025/26
- 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 |
|
| Hours |
|
| 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 3 and 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 jointly with the other written part of module II. FOR ATTENDING STUDENTS: two partial tests are foreseen with the same overall verification methods relating to the practical test in R, but based only on the first or second part of the course, respectively. The average mark of the two parts will contribute to establishing the admission mark or not to the oral exam which must be taken by the last session of the first useful exam session. In the overall judgment, the practical part and the oral exam have equal importance. 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. |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile |
PROBABILITY AND STATISTICS - II MODULE
| Code | A001547 |
|---|---|
| CFU | 6 |
| Teacher | Andrea Capotorti |
| Teachers |
|
| Hours |
|
| 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 | Q. Berger, F. Caravenna, P. Dai Pra, Probabilità Un primo corso attraverso esempi, modelli e applicazioni, Springer P. Baldi, Calcolo delle Probabilità, McGraw-Hill, seconda edizione, 2011. S. Ross, Calcolo delle Probabilità, Apogeo, Maggioli Editore (translation of the English version "A First Course in Probability") 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. Further teaching material, such as updated notes from the lecturer and solving of the proposed exercises and past exam papers, is available on Unistudium. |
| Educational objectives | This course is the first approach to Probability and is aimed at giving the students a good understanding of the basic elements of Probability Theory through rigorous definitions, theorems and proofs. 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. The student will be able to describe, link and compare the main statements and results given and to show the theorems considered. She/he will solve problems relating the theoretical expertise with the selection and building of models following the guidelines given in the practice lessons. |
| Prerequisites | Here's the English translation of the text: Basic notions of mathematical analysis, with particular attention to differential and integral calculus, and numerical sequences and series. Basic notions of algebra and combinatorial calculus. To best understand the topics of this course, the concepts developed in the Mathematical Analysis I and II courses are fundamental. |
| Teaching methods | The course is structured as follows: - lectures covering all program topics; - discussion and resolution of exercises related to all program subjects. |
| Other information | 1) Attendance at lectures is not mandatory, but it is highly encouraged. 2) 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 | The exam consists of a written test and an oral exam: The written test, which typically lasts between one and two hours, includes exercises designed to assess problem-solving skills for practical and theoretical problems and covers all topics covered during the course Students who score at least 18/30 on the written test can access the oral exam, which has an approximate duration of 30 minutes. This exam covers the entire course program and aims to evaluate presentation skills, the appropriate use of fundamental techniques and concepts, and the depth of study. Students may request to take the exam in English. Students with Specific Learning Disorders and/or Disabilities can refer to the we page: http://www.unipg.it/disabilita-e-dsa. |
| Extended program | Theoretical notions of probability: events, conditional probability, independence. Bayes' theorem. Random variables, probability distributions, cumulative distribution function and probability density function, discrete and absolutely continuous random variables and their properties. Expected value and variance. Functions of random variables. Joint distributions of random variables. Concentration inequalities. Law of large numbers and central limit theorem. Moment-generating function. |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile |