Syllabus - Statistics I

Author

Paulo Fagandini

Bachelor’s Degree in Management
Course Director: Professor Dr. Maria Teresa Fortunato Pereira Esteves
Academic Year: 2025/2026

Course Unit: Statistics I - English Track
Field: Data Science and Statistics
Course Coordinator: Sandra Custódio

Instructor: Paulo Fagandini
Year/Semester: 2nd Year / 3rd Semester
Weekly Hours: 3 Hours
ECTS: 4

General Objective

At the end of the course, students should understand index number theory, acquire basic concepts of random variables, and be able to identify and apply key probability models in the context of random phenomena. The main goal is to convey these concepts in a way that enables reasoning in uncertain environments and supports learning other statistical techniques.

Competencies

Students should:

  • Understand methodologies related to index numbers, probabilities, random variables, and parameters.
  • Acquire skills for the combined use of different statistical techniques to obtain results that support decision-making in random environments.
  • Be able to use the main statistical techniques to perform analyses and interpret results in business and institutional contexts.

Learning Outcomes

The student should:

  • Master the methodology of index numbers within the context of key economic and financial indicators.
  • Master the fundamental concepts of probability theory and calculate probabilities associated with random phenomena.
  • Be able to characterize random variables and identify their probability distributions.
  • Gain competence in combining various statistical techniques to support decision-making in uncertain environments.

Syllabus

  1. Index Numbers
    1. Introduction. Definition of Simple Indexes and Growth Rates
    2. Index Series: Fixed Base and Moving Base
    3. Properties of Simple Indexes
    4. Composite Index Numbers. Concept of Basket. Consumer Price Index (CPI)
    5. Composite Index Series: Fixed Base and Moving Base
    6. Desirable Properties of Composite Indexes. Problems in constructing index numbers
  2. Probability, Random Variables, Probability Distributions, and Population Characteristics
    1. Concepts of Random Phenomena, Random Experiments, Sample Space, and Events
    2. Concepts of Probability. Kolmogorov AxiomsStatistics I - Course Syllabus (2024/2025)
    3. Conditional Probability. Probabilistic Independence
    4. Law of Total Probability and Bayes’ Theorem
    5. Concept of Random Variable: Discrete and Continuous
    6. Probability Mass Function, Probability Density Function, and Distribution Function
    7. Discrete Random Pairs: Joint Probability Function, Marginal Function, Independence
    8. Population Characteristics: Mean, Variance, Standard Deviation and properties; Quantiles; Covariance and Correlation Coefficient
  3. Probability Models
    1. Discrete Probability Models
      1. Bernoulli and Binomial Distributions. Additivity Theorem
      2. Hypergeometric Distribution and its Approximation to Binomial
      3. Geometric Distribution. Memoryless Property
      4. Poisson Distribution. Additivity Theorem. Approximation from Binomial
    2. Continuous Probability Models
      1. Uniform Distribution
      2. Exponential Distribution and its Properties
      3. Normal Distribution and its Properties. Additivity Theorem

Assessment Methods

Assessment may be continuous or through a final exam.

Continuous Assessment

Assessment Element Weight (%) Duration Syllabus Date
Midterm 1 60% 80 minutes Topics 1 and 2 Nov 6th
Midterm 2 40% 80 minutes Topic 3 Dec 11th

Notes:

  • Continuous assessment includes two in-person written tests (Midterm and Exam).
  • Students must score at least 7/20 on each test and attend all evaluation sessions (not 6.9 or 6.99).
  • Students qualifying for the continuous assessment may choose to take the Partial Exam during the regular exam period. Alternatively, they can choose to take the Full Exam.
  • If the partial exam is chosen, the final grade will be a weighted average: Final Grade = 0.6 Midterm + 0.4 Partial Exam
  • There is no minimum attendance requirement.

Final Exam Assessment

Students may opt for a final exam worth 100% of the grade, covering the entire syllabus.

Core Bibliography (PT)

  • Ferreira, T., Custódio, S.G. (2023) Modelos Probabilísticos, Edições Sílabo
  • Gancho Custódio, S. et al. (2022) Números Índices, Edições Sílabo
  • Murteira, B. et al. (2010) Introdução à Estatística, McGraw-Hill

Bibliography (EN)

  • Ralph, J. et al. (2015) A Practical Introduction to Index Numbers, 1st Ed, Wiley.
  • Newbold, P. et al. (2023) Statistics for Business and Economics, 10th Global Edition, Pearson.

Complementary:

  • Black, K. (1992) Business Statistics, West Publishing Company
  • Harnett, D.L. & Murphy, J.L. (1980) Introductory Statistical Analysis, Addison-Wesley
  • Ingram, J.A. & Monks, J.G. (1992) Statistics for Business and Economics, The Dryden Press
  • Wooldridge, J.M. (2009) Introductory Econometrics, Thomson South-Western

Bibliography (PT):

  • Murteira, B. (1993) Análise Exploratória de Dados, McGraw-Hill
  • Paulino, C. & Branco, J. (2005) Exercícios de Probabilidade e Estatística, Escolar Editora
  • Pedrosa, A.C. & Gama, S.M.A. (2004) Introdução Computacional, Porto Editora
  • Pimenta, F. et al. (2015) Introdução à Estatística, Escolar Editora
  • Robalo, A. (1995) Exercícios de Estatística, Edições Sílabo