PROBABILITY: PROBLEMS AND EXERCISES

Course Sheet

Course code:

000180L

Academic Year of enrolment:

2022

Year of supply:

2022/2023

Degree:

Course of 1st Cycle Degree in ECONOMICS AND COMMERCE

Disciplinary Sector:

Probability and Mathematical Statistics

Location:

PESCARA

Credits:

Programme Year:

Professor and Collaborators:

CAROLI COSTANTINI Cristina

Cycle:

Second semester

Hours of classroom activity:

Individual study hours:

Prerequisites:

Basic notions of differential and integral calculus and of vectors and matrices.

Objectives

This is the companion course of the Probability course and aims at giving the student the essential tools to analyse random phenomena, by working out exercises, and at developing the ability of the student to apply her/his knowledge to problem solving.

EXPECTED LEARNING RESULTS.
The student is expected to:
- acquire the essential tools to analyse random phenomena;
- be able to formalise and solve problems (problem solving);

KNOWLEDGE AND ABILITY TO UNDERSTAND:
At the end of the course, the student should have:
- understood the fundamental concepts of Probability;
- acquired the essential tools to analyse random phenomena;
- developed the ability to formalise problems and solve them (problem solving);

Contents

Exercises and problems on: probability spaces; elements of combinatorics and uniform, finite probability spaces; conditional probability and independence; discrete and absolutely continuous random variables; pairs of discrete and jointly absolutely continuous random variables; jointly Gaussian random variables; law of large numbers, central limit theorem.

Extended Syllabus

1. Probability spaces and their properties. Finite, uniform probability spaces. Combinatorics. extractions without replacement.

2. Conditional probability and its properties. Bayes formula. Independent events and conditionally independent events. Bernouli trials.

3. Discrete random variables: binomial, hypergeometric, geometric and Poisson laws.

4. Continuous random variables: uniform, exponential and Gaussian laws. Distribution function.

5. Expectation and its properties. Variance. Quantiles.

6. Joint laws of random variables: marginals, independence, conditional density. Density of the sun of two random variables. Sum of independent Gaussian random variables.

8. Joint Gaussian distributions.

9. Law of large numbers and Central Limit Theorem.

Recommended Bibliography

S. Ross: Calcolo delle probabilità 3/ed, Apogeo, 2014
Notes and exercises available on the web page of the teacher (https://economia.unich.it/). The textbook is also available in English and the on-line material is available in English, upon request.

Teaching Methods

The course is organized in at least 24 hours of lectures where exercises and applications are presented, and exercises and problems, previously assigned as homework, are worked out.
Attendance is optional but suggested and the final exam, which will be joint with the final exam of the Probability course, will be the same for attending and non attending students.

Evaluation methods

Verification of learning:

There will be a joint final exam for the courses of Probability and Laboratory of Probability. The final exam will consist of both a written test and an oral exam. The written test will be composed of exercises and problems. Both the written text and the oral exam can be taken in English.
The final evaluation will be expressed as "approved" or "not approved".

Contacts/More Information

Weekly office hours: see the teacher web page https://www.dec.unich.it/home-caroli-costantini-cristina-146
E-mail: c.costantini@unich.it
Office hours can also be in English.

Università degli Studi
"G. d'Annunzio"

Chieti - Pescara

Aree