Select Academic Year:     2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022
Second Semester 
Teaching style
Blend/modalità mista, Convenzionale 
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


The importance of statistical procedures for business applications is increasing, also as a result of digitalization. In this context, it is important to extract information from the data and to assess its reliability. The course aims to teach the main techniques for data description useful to gain knowledge from data and the basic principles of probabilistic and inductive reasoning useful to take principled decisions in uncertain context. Doing so, it builds the standard core of knowledge for courses on business statistics, financial statistics and other specialized topics. An optional part will introduce the R language for statistical computing.

Expected learning outcome (knowledge and understanding):

At the end of the course students learn the assumptions and understand the rationale behind statistical techniques. Students learn basic data analysis techniques, main probability models and inferential procedures. The R lab develops basic coding skills (optional).

Expected learning outcomes (applying knowledge and understanding):

Having successfully completed the course students are able to choose the appropriate descriptive or inferential statistical procedure for the problem at hand; they should be able to apply a technique, to interpret the result and to draw conclusions. In particular, students should be able to

- synthetize a dataset using graphical, tabular and numerical measures;
- formalize and solve problems involving uncertainty using probability calculus;
- perform statistical tests, find point or confidence estimate of a population parameters assessing the uncertainty of the results;
- use R to deal with previous topics


A one-semester course in mathematics for undergraduate students in economics.


Course Content

Part 1 (Descriptive Statistics)

The statistical survey and its main phases. Statistical sources. Statistical units. Population and sample.
Quantitative and qualitative statistical variables.
Graphical representation of data.
Measures of central tendency and variability. Shape of a distribution.
Bivariate joint frequency distributions, marginal and conditional frequencies. Statistical independence.
Analysis of linear correlation, Pearson correlation coefficient. Interpolation: the method of least squares.

Part 2 (Elements of probability theory)

What is probability? Events, logical operations on events.
Elementary theorems of probability theory. Conditional probability and Bayes Theorem.
Random variables. Cumulative distribution function, probability and density functions.
Mathematical expectation and variance of a random variable. Chebycev inequality.
Discrete random variables: Uniform, Bernoulli, Binomial, Hypergeometric, Poisson.
Continuous random variables: Uniform, Normal.
Functions of random variables, in particular linear function. Bivariate random variables. Joint probability distributions, marginal and conditional distributions. Stochastic independence. Functions of random vectors, in particular linear function. Central Limit Theorem.

Part 3 (Sampling and statistical inference)

Population and sample. Some statistics and their sampling distribution. Sample mean and variance. Outline of sampling techniques.
Parameter estimation. Main properties of point estimators.
Interval estimate. Confidence intervals for large samples.
Hypothesis testing. Outline on the construction of a test: the decision-making approach and the Neyman-Pearson strategy. Test statistics, type I and type II errors, power of a test. The pvalue.
Hypothesis testing for mean and proportions and their difference (paired and unpaired samples).
Goodness-of-fit test for univariate and bivariate distributions (independence test).
The linear model: some historical notes. Weak and strong assumptions. Least square estimators of the parameters. Deviance decomposition and goodness of fit. Sample distribution of beta_1_hat: ci and inference on beta_1. Reading the linear model output from a statistical package

Teaching Methods

Lectures (72 hours) and practice sessions (20 hours). Total credit: 12 CFU.

Teams code for all lectures: tba

Verification of learning

The test is organised as follows:

- a written test (up to 30 points)
- an optional oral exam (up to 3 points)
- an optional test on R/Radiant (up to 3 points)

If the student passes the written exam his final score is fS=Ws*28/30+Os+Rs (possibly rounded)

The written exam can be fulfilled by a general exam or by two partial exams, one at the half and the other at the end of the course (scheduled together with the first general test).

To pass the written part the student should score i) at least 17 on a general test or ii) an average of at least 17 points on the two partial tests, provided that each test is at least 16 points.

The oral exam is dedicated to proofs of some important results. See the detailed program for the list of proofs.

The R test requires students to analyse a data set using R/Radiant.

All exams and homeworks are graded according to the extent the student demonstrates i) understanding of theoretical concepts ii) the ability to apply them, also using R/Radiant iii) correct interpretation of results iv) the ability to clearly present an argument.

There are no differences between attending and non attending students.


Newbold P., Carlson W., Thorne, B. Statistica
3rd (if available) or 2nd italian edition (translation of the Pearson 7th English edition). Erasmus students may prefer to study from the original english edition.

More Information

Further teaching material for class 3 is available from link below, including past exams, book slides, practice session exercises, R scripts and a detailed syllabus with the list of proofs for the oral part. Some of the instructor's notes will be available on teams.

The material in the section will be updated during the course so please check it periodically.

Link to class material:

see the Italian page

Other links:
(it will be occasionally used for illustrative purpose)

NB: The course is taught in Italian. Students whose mother tongue is not Italian may find profitable to study from the English edition of the book. Please contact the instructor for further help.

Questionnaire and social

Share on: