
Course unit
PROBABILITY AND STATISTICS
SC03106737, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/06 
Probability and Mathematical Statistics 
6.0 
Course unit organization
Period 
Second semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
16 
34.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Prerequisites:

Familiarity with the basic notions of analysis, linear algebra and combinatorics. The courses "Analisi matematica" and "Algebra e matematica discreta" cover all the necessary prerequisites. 
Target skills and knowledge:

The student will acquire a basic knowledge of probability theory and inferential statistics. Those that will pass the exam will be able to build simple probabilistic models of uncertain phenomena and carry out the necessary probabilistic and/or statistical computations. 
Examination methods:

3 hour written test (closed book). 
Assessment criteria:

The student will have to master the theoretical concepts and show his ability to apply them to solve problems of probability and statistics of appropriate difficulty. 
Course unit contents:

Probability theory. Axioms and their elementary consequences. Examples of discrete, finite, and uniform probability spaces. Combinatorics. Conditional probability. Law of total probability and Bayes formula. Independent events. Discrete random variables. Probability mass function. Moments: expectation, variance and higher order moments. Examples of discrete random variables: Bernoulli, binomial, geometric and Poisson distributions. Poisson limit theorem. Discrete random vectors. Joint and marginal discrete densities. Expectation of real functions of discrete random vectors. Covariance. Independent discrete random variables. Absolutely continuous random variables. Probability density function and distribution function. Moments: expectation and variance. Examples of absolutely continuous random variables: uniform, exponential and normal distributions. Limit theorems. Weak law of large numbers. Monte Carlo method. Central limit theorem. Normal approximation.
Descriptive statistics. Qualitative and quantitative data, relative frequencies, graphical methods. Empirical indices: location, centrality, dispersion, shape. Correlation between variables: regression line, covariance and correlation coefficient.
Inferential statistics. Estimators. Confidence intervals. 
Planned learning activities and teaching methods:

Traditional lectures. A typical lecture is aimed at transmission of theoretical contents, illustration of examples and solution of exercises. Through the moodle platform homework assignments are proposed weekly and then solved. 
Additional notes about suggested reading:

The lectures cover all the topics on which the exam is based. The moodle platform contains several teaching aids: additional references, notes and several sheets of exercises with their solutions. 
Textbooks (and optional supplementary readings) 

Finesso, Lorenzo, Lezioni di probabilità. Padova: Libreria Progetto, 2017.

Ross, Sheldon M., Introduzione alla statistica. Milano: Apogeo, 2008.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex

