C8399 - REFRESH COURSE DI PROBABILITA' E STATISTICA

Learning outcomes

By the end of the course, students will be able to recall, understand and apply the key concepts of probability and statistics that constitute prerequisites for the courses included in the degree programme.

Students will also acquire or consolidate the basic matrix algebra skills required to understand statistical notation and methods.

Course contents

The course reviews and consolidates the main concepts of probability, statistics and matrix algebra required for the courses included in the degree programme. The following topics will be covered:

1. Probability

• the concept of probability;
• probability axioms;
• the law of total probability;
• Bayes’ theorem.

2. Random variables

• definition of a random variable;
• discrete random variables and the main discrete distributions, with particular reference to the Bernoulli and binomial distributions;
• continuous random variables and the main continuous distributions, with particular reference to the uniform and normal distributions;
• properties of expected value and variance.

3. Multivariate distributions

• bivariate random variables;
• joint and marginal distributions;
• conditional distributions;
• independence;
• covariance and correlation;
• the multivariate normal distribution.

4. Sample statistics and point estimation

• populations and simple random samples;
• parameters, sample statistics and estimators;
• the sample mean;
• sampling distributions and sample space;
• main properties of estimators.

5. Confidence intervals

• principles of interval estimation;
• confidence intervals for the mean, variance and proportion.

6. Hypothesis testing

• formulation of statistical hypotheses;
• Type I and Type II errors;
• one-tailed and two-tailed tests;
• tests based on the normal and Student’s t distributions;
• significance level and p-value.

7. Matrix algebra

• definition and main types of matrices;
• matrix operations;
• trace;
• rank and inverse matrix.

Readings/Bibliography

There is no compulsory textbook. The teaching materials used during the course, including slides, exercises and any supplementary readings, will be made available through the Virtuale platform.

Additional bibliographical references may be provided during the course.

Teaching methods

The course consists of lectures and guided exercise sessions. The presentation of theoretical concepts will be accompanied by examples and exercises to review and consolidate students’ basic knowledge of probability, statistics, and matrix algebra.

Particular attention will be paid to the practical application of the concepts and to problem-solving.

Assessment methods

The achievement of the learning outcomes will be assessed through exercises and short self-assessment tests proposed during or at the end of the different course units.

The course is designed to review and consolidate prerequisite knowledge and does not include a final graded examination.

Teaching tools

Lectures will be supported by slides, summary materials, examples and exercises. All teaching materials and course-related communications will be made available through the Virtuale platform.

Office hours

See the website of Silvia Bianconcini