Degree course: 
Corso di First cycle degree in ECONOMICS AND MANAGEMENT
Academic year when starting the degree: 
Academic year in which the course will be held: 
Cognomi A-G
Second semester
Standard lectures hours: 

The topics covered in the course of Mathematics (code ECO0011)


With the purpose of measuring the acquisition of the above-mentioned learning outcomes, the students’ assessment is based on a written exam concerning theory and exercises.
The general written exam consists of 8 multiple choice questions (max points: 8/30) and 3 or 4 exercises (max points: 22/30) aimed to assess students’ ability to apply properly the statistical tools illustrated during the course, to summarize information contained in datasets, to study the relationship between variables, to choose adequate probability models as well as to estimate unknown parameters.
Students have the opportunity (not compulsory) to prepare a PC project (max points: 2/30) aimed to test the students’ ability to analyze a real dataset with Excel and discuss critically the output.
Alternative to the general written exam, students can take two partial written exams (one in the middle of the semester and the second at the end of the course).

Voto Finale

Students will acquire a good understanding of the statistical tools and techniques related to descriptive statistics, probability and inferential statistics covered in the course, as well as the ability to employ them in economic and business applications.

At the end of the course students will be able to:
-Understand the fundamentals of statistical thinking, both descriptive and inferential.
-Reproduce the basics of descriptive and inferential statistics to economic data analysis.
-Summarize and visualize information contained in real data sets.
-Study the relationship between relevant variables.
-Choose adequate probabilistic models to represent data and learn from it in a statistical setting.
-Estimate unknown population parameters based on sampling information.
-Interpret the obtained results.

−Classification of the variables
−Absolute, relative and percentage frequencies.
−Graphical representation of the variables:
1. Pie charts, bar charts, histograms.
2. Cumulative distribution function.

−Numerical description of the variables:
−Measures of central tendency: analytic means (arithmetic and geometric mean); median and quartiles, mode.
−Measures of variability.
−Concentration measures.

−Bivariate analysis:
−Scatter plot and contingency table. Joint, marginal, conditional distributions. Conditional mean.
−Chi-square measure of association
−Linear dependence between two variables: covariance and correlation coefficient.

- Simple linear Regression:
- Ordinarily least square estimators
- Prediction
- R2 coefficient of determination.

- Examples and applications of some descriptive statistics tools with Excel.

Random variables (r.v.):
−Review of Bernoulli, Binomial, Poisson distributions.
−Review of uniform, normal, exponential distributions.

Point estimation
−Random sample, estimator and estimate: definition.
−Sample mean and sample variance: definition and properties.
−Central Limit Theorem
−Properties of estimators: unbiasedness, asymptotic unbiasedness, efficiency, consistency.

Confidence Intervals
−Definition of Confidence Intervals (C.I.)
−C.I. for the mean of the normal population: variance known and unknown; Student T distribution.
−C.I. for the proportion of a Bernoulli population.

Test of Hypothesis
−Test for the mean of the normal population: variance known and unknown
−Test for the proportion of the Bernoulli population.
−Test for the variance of the normal population.

Two populations
−C.I. and test for the difference in the means of two normal populations: variance known and unknown.

- G. CICCHITELLI, P. D’URSO, M. MINOZZO (2017), Statistica: principi e metodi, Terza edizione, Pearson Italia, Milano (Chapters 1-6; 9-11; 13 - 14; 16 - 21)
- Notes and additional exercises will be available on e-learning page.

The theoretical lessons will be accompanied by weekly exercises classes.

Updated information about the office hour are available at the Professor's web page.