Insegnamento a.a. 2024-2025

20356 - STATISTICS - PREPARATORY COURSE

Department of Decision Sciences

Course taught in English

Student consultation hours
Class timetable
Exam timetable
Go to class group/s: 1
DES-ESS (I sem. - P) - DSBA (I sem. - P) - CYBER (I sem. - P)
Course Director:
IGOR PRUENSTER

Classes: 1 (I sem.)
Instructors:
Class 1: MARCO UGO CLAUDIO BOELLA


Suggested background knowledge

The course will start from the basic concepts of probability; still some previous knowledge of elementary probability tools is beneficial, even if not strictly necessary. On the other hand, a good level of familiarity with calculus techniques (derivatives, integrals, numerical series, …) is required.

Mission & Content Summary

MISSION

The aim of this preparatory course is to establish a sound basis for the following advanced statistics courses. To this end the basic concepts and techniques of probability theory, which will be leveraged upon in the regular courses, are reviewed and illustrated in detail, with examples illustrating their implementation. The course provides a stand-alone corpus of notions of probability theory, which are essential for principled statistical inference.

CONTENT SUMMARY

  • Basic probability, conditional probability, independence.
  • Random variables: discrete and continuous random variables, expectations and variances, transformations of random variables.
  • Common families of random variables.
  • Random vectors: discrete and continuous random vectors, joint and marginal distributions, independent distributions, moments and covariances, bivariate transformations of bivariate vectors.
  • Conditional distributions and conditional expectations.
  • Variables arising from normal sampling.
  • Sequences of random variables: introductory concepts of convergence.

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Define the basic concepts of probability and conditional probability.
  • Identify families of random variables (and random vectors) and illustrate their role in modeling.
  • Express and explain the basics of sampling

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Use families of random variables to model (stylized) real phenomena
  • Compute expectations and variances of various probabilistic models
  • Interpret statistical inference from a probabilistic point of view

Teaching methods

  • Lectures
  • Practical Exercises

DETAILS

Face-to-face lectures


Assessment methods

  Continuous assessment Partial exams General exam
  • Active class participation (virtual, attendance)
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ATTENDING AND NOT ATTENDING STUDENTS

There is no formal assessment for this course


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Any basic textbook on probability theory and mathematical statistics would be appropriate. For instance:

  • A.MOOD, F.A.GRAYBILL, D.C.BOES, Introduction to the Theory of Statistics, McGraw Hill, 1974.

Moreover, many advanced statistics textbooks have some introductory chapters about basic topics. For instance:

  • N. MUKHOPADHYAY, Probability and Statistical Inference, Dekker-CRC press, 2000.
  • G. CASELLA, R.L. BERGER, Statistical Inference, 2nd Ed., Duxbury, 2002
Last change 12/04/2024 16:21