Statistics I (Erasmus section)

Syllabus and Course Information

Author
Affiliation

Paulo Fagandini

ISCAL-IPL

General Information

Instructor Paulo Fagandini
Email pfagandini@iscal.ipl.pt
Academic Year 2026/2027, 1st semester
ECTS 4
Section Erasmus (taught in English)
Schedule Thursday, 11:00-14:00
Format 11 lecture sessions of 3 hours + 2 assessment sessions
Course material Moodle@ISCAL
Official communication channel Institutional email
Note

The Erasmus section begins one week after the Portuguese sections. The first session is Thursday 17 September 2026.

Syllabus

Topic 1: Growth Rates and Index Numbers

  1. Growth rates: simple, accumulated and average growth rates
  2. Simple index numbers: base period, rolling base, chain and link indices, base change
  3. Properties of a good index: identity, time reversal, factor reversal, circularity
  4. Composite (aggregate) index numbers: baskets, Laspeyres, Paasche and Fisher indices
  5. Application: the Consumer Price Index, the HICP and the measurement of inflation

Topic 2: Probability and Random Variables

  1. Set theory refresher: sets, operations, partitions
  2. Sample space, events, and the classical and frequency interpretations of probability
  3. Probability axioms and their corollaries
  4. Conditional probability, independence, the Law of Total Probability and Bayes’ theorem
  5. Random variables: discrete and continuous; probability density and cumulative distribution functions
  6. Moments of a population: expected value, quantiles, variance, standard deviation, coefficient of variation
  7. Random pairs: joint and marginal densities, independence, covariance and correlation

Topic 3: Probability Models

  1. Discrete models: Bernoulli, Binomial, Hypergeometric, Geometric and Poisson
  2. Relationships between discrete models: Hypergeometric → Binomial, Binomial → Poisson
  3. Continuous models: Uniform and Exponential (memorylessness)
  4. The Normal distribution: standardization, table reading, additivity and corollaries

Assessment

Continuous Assessment

Two in-person written tests. Each test carries a minimum grade of 7.00 out of 20. The weighted average must be 9.50 or higher to pass.

Test Weight Duration Content
Midterm 1 60% 80 minutes Topics 1 and 2 (points 1 to 12)
Midterm 2 40% 80 minutes Topic 3 (points 13 to 16)

Midterm 1 takes place in Session 8 and Midterm 2 in Session 13 (see the Calendar section for the dates).

Warning

There is no make-up date for the midterms. A student who misses one must sit the Comprehensive Exam.

Comprehensive Exam

Students may opt, on the day of the exam, to sit a Comprehensive Exam worth 100% of the grade, covering Topics 1, 2 and 3. Students who do not complete continuous assessment, or who score below 7.00 in a midterm, are assessed this way.

Exam Rules

  • Calculator: only a basic scientific calculator is allowed. Graphing calculators are not permitted.
  • Personal belongings: bags must be left at the front of the room and phones stored inside them.
  • Electronic devices: using earphones, headphones, a smartwatch, a smartphone or any electronic device during the test counts as fraud, implying failure in the course unit and a report to the School for disciplinary purposes.
  • Complementary oral examination: the teaching staff reserves the right to call a student for a complementary oral examination whenever doubts remain about the grade. The final grade may be adjusted following that examination.

Calendar

All sessions are on Thursday, 11:00-14:00. Dates are day/month, 2026.

# Session Date
1 Course information; growth rates; index numbers: definition and simple index 17/09
2 Rolling base, chain and link indices, base change, tests for simple indices 24/09
3 Composite indices: Laspeyres, Paasche, Fisher; CPI, HICP and inflation 01/10
4 The concept of probability; set theory refresher; sample space and events 08/10
5 Interpretations of probability; axioms; conditional probability 15/10
6 Independence, Total Probability, Bayes; random variables, density and distribution functions 22/10
7 Moments; random pairs, covariance and correlation; consolidation 29/10
8 MIDTERM 1 (Topics 1 and 2) 05/11
9 Bernoulli, Binomial and Hypergeometric models 12/11
10 Geometric and Poisson models 19/11
11 Uniform and Exponential models; the Normal distribution 26/11
12 The Normal distribution; revision and exam guidance 03/12
13 MIDTERM 2 (Topic 3) 10/12

Calendar notes:

  • No Portuguese public holiday falls on a Thursday during the teaching period, so no session is lost. For reference, the holidays in the period are 05/10 (Implantação da República, a Monday), 01/12 (Restauração da Independência) and 08/12 (Imaculada Conceição, both Tuesdays).
  • The teaching period runs from 07/09/2026 to 15/12/2026; 10/12 is therefore the last available Thursday.
  • Midterm dates are confirmed on Moodle. Where this page and Moodle disagree, Moodle is correct.

Bibliography

Reference texts

  1. Gancho Custódio, S., Ferreira, T., António, S. and Caldeira, O. (2022). Números Índices: Exposição Teórica e Exercícios, 2nd revised and expanded edition. Edições Sílabo.
  2. Ferreira, T. and Gancho Custódio, S. (2023). Modelos Probabilísticos. Edições Sílabo.
  3. Murteira, B., Silva Ribeiro, C., Andrade e Silva, J. and Pimenta, C. (2010). Introdução à Estatística. Escolar Editora / McGraw-Hill.

In English

  1. Newbold, P., Carlson, W. and Thorne, B. (2022). Statistics for Business and Economics, Global Edition, 10th ed. Pearson.
  2. Fisher, I. (1922). The Making of Index Numbers, 1st ed.
  3. Ralph, J., O’Neill, R. and Winton, J. (2015). A Practical Introduction to Index Numbers.

Correspondence with the Bibliography

For each topic, the table gives the supporting readings. The lecture slides are the primary reference; an empty cell means that book does not develop the topic.

Topic Theme Newbold et al. Edições Sílabo
1 Growth rates and index numbers Números Índices
2 Probability, set theory, Bayes Ch. 3 Introdução à Estatística
2 Random variables and moments Ch. 4, 5 Introdução à Estatística
3 Discrete probability models Ch. 4 Modelos Probabilísticos
3 Continuous probability models Ch. 5 Modelos Probabilísticos

Slides

For each deck: title = the presentation · [📄] slide PDF · [🌐] web version (single scrollable page with a table of contents, easier for reviewing or printing than clicking slide by slide).

Topic 1: Growth Rates and Index Numbers

  1. Introduction and Growth Rates 📄 🌐

Topic 2: Probability and Random Variables

  1. Introduction to Probability Theory 📄 🌐
  2. Random Variables 📄 🌐

Topic 3: Probability Models

  1. Discrete Probability Models 📄 🌐
  2. Continuous Probability Models 📄 🌐

Problem Sets

Self-checking exercises: fill in the blank, multiple choice and true/false, with hidden solutions you can reveal in place.

  1. Chapter I: Growth Rates and Index Numbers
  2. Chapter II Part I: Introduction to Probability Theory
  3. Chapter II Part II: Random Variables
  4. Chapter III Part I: Discrete Probability Models
  5. Chapter III Part II: Continuous Probability Models

Acknowledgement

These slides are a free translation and adaptation of the slide deck for Estatística I by Prof. Sandra Custódio and Prof. Teresa Ferreira, Lisbon Accounting and Business School, Polytechnic University of Lisbon.