Scheda programma d'esame
Academic year2022/23
PeriodSemester 1

Programma non disponibile nella lingua selezionata
Learning outcomes
  • To endowe students with a solid knowledge in fundamental statistical theory and operative feeling with its main ideas, including:

    –the development of a solid background for subsequent  exams  in this area such as econometrics and applied statistics, in particular within the "Official  statistics" curricula,

    –a background of ideas from probability theory and probability modeling

    –tools of general statistical reasoning to assist the entire students career and working life     


Assessment criteria of knowledge

Given the international nature of the course and the pool of different background at entry, in this course there is a long tradition  - unique in this university - of individual and group meetings between the instructor and the students (typically during the first 3 weeks of the course) aimed to allow the instructor to assess the students' initial conditions, the possible presence of entry gaps, and to appropriately define the course targets given the abilities of the audience. The instructors (PM and CG) have always encouraged the creation of spontaneous study groups to handle assignments through active discussions between peers.

The final abilities will be assessed by a written exam including both theoretical (e.g., definitions, theorems, proofs etc) and applied questions.


On successful completion of this course students will dispose of a solid background of fundamental statistical theory and ability to implement the methodologies using real or simulated data.

Assessment criteria of skills

During the entire flow of the course day-to-day assignments are foreseen, so that students it will be possible for the students as well as for the instructors to have real time update of learning progresses.


To fully benefit of the course (i.e. to develop a feeling of statistical reasoning and attitudes towards the use and interpretation of data) students are strongly recommended to attend lectures intensively, to solve assignments in real-time, to actively discuss with their colleagues on the course topics.

Very important: given the international status and audience of the course, students will be asked  to give availability to provide assistance  and tutoring to their colleagues from foreign countries.

Assessment criteria of behaviors

Day by day.


These are minimal requirements necessary to benefit of the course. Do you fulfill them ? (answer honestly...)

  • Mathematics: working knowledge in basic calculus (elementary mathematical functions, basics of optimization, basic integration).
  • Basic descriptive statistics: basic summary measures for 1- and 2-variate observations including mean, median, percentiles, variance & standard deviation, chisquare, correlation coefficient, and least square regression.
  • Basic probability: basic notions of probability theory and noteworthy distributions especially the binomial and the normal distribution.
  • Basic statistical inference: basic notions of interval estimation and testing.
  • Working knowledge of electronic sheet (eg excel or calc) highly recommended as a tool for nontrivial implementation and visualization of concepts.
  • IMPORTANT: online materials for refreshing basic concepts of statistics and probability will be made available before the start of the course.
Teaching methods

Ex-cathedra lectures using slides complemented by "choke and blackboard" for solving examples and exercises. Day-to-day assignments (to be solved in real time to fully benefit of the course contents). Computer sessions.

How to prepare the exam:

–following lectures actively. Slides are made available a few days after the corresponding lecture on the new e-learning page:

–doing carefully assignments and exercises (on a day-by-day basis…).

Exercises and assignments are an integral part of the course. They are planned to set in practice the concepts developed day-by-day during lectures, and to follow smoothly the development of the various subjects. Do not neglect them ! 

  • Probability & modeling

–Refreshment of basic probability ideas. Random variables & their characterization. Distribution functions and expectations. Moment generating function & other auxiliary functions.

–Main discrete & continuous distributions. Elementary probability modeling. Hazard models.

–Random vectors & functions of random variables.

–Asymptotics. Central limit theorem, law of large numbers.

  • Likelihood based inference

–Sampling. Estimation. Likelihood-base inference. Point estimators. Computing maximum likelihood estimators. Properties of point estimators.

–Confidence intervals. Likelihood based (profile) vs pivotal approaches.

–Test of hypotheses.

–Goodness of fit. BIC. Likelihood ratio test.

  • (some) Advanced topics

- Modern computer-based statistics. Basic bootstrap (using R) software.

–Introduction to probability modeling: finite Markov chains & the Poisson process.

–Basic ideas of Bayesian inference.


Class slides made available within 2-3 days after the corresponding lecture. 

Main Course Textbook. Mood AM, Graybill, Boes D (1981), “Introduction to the theory of statistics”, Mc Graw Hill (some editions available online). A very complete reference book. It covers 80% of the course topics. Important you always keep it open in your laptop…

Other readings to be communicated during the Course.

Non-attending students info

Neither foreseen nor recommended for this course. Anyhow the course materials  are largely self-contained.

Information for students unable to attend class lecture due to the COVID situation will follow online activities according to the general rule of this MSE ( 

Additional web pages

Official e-learning page of the course (moodle portal):


Updated: 19/09/2022 13:23