Statistical Methods

Year
2
Academic year
2019-2020
Code
01006051
Subject Area
Applied Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

Recommended Prerequisites

Calculus I, (Calculus II).

Teaching Methods

Essentially based on classes with a mixed T and TP character, in which the presentation of the theory is imediately followed by the resolution of some problems of application, according wOs ith the pedagogical strategy presented in 3.3.6.

Learning Outcomes

1. Understanding of a probabilistic/statistic prediction of a phenomenon, distinguishing it from a deterministic prediction (already familiar) and being able to recognize the cases when it becomes interesting or even necessary; and

2. Capacity to perform some probabilistic and statistical analyses of phenomena (see 3.5), making use of the mathematical theories of Probability and Inferential Statistics. The focus is put on the ability to apply the theory in a versatile, effective and sure way to solve a great variety of practical problems of interest in any field of engineering and in life in general.

Work Placement(s)

No

Syllabus

0. Why to study Probability and Statistics in engineering?

1. PROBABILITIES. 1.1. Concepts of random exp. and probability (Classical, Empirical), Laws of probability. 1.2. Random variables. 1.2.1. Concept and forms of charact. (Probability, Probab. density and Distribution Functions, Moments), and concept of probab. model. 1.2.2. Discrete models: Uniform, Binomial, Poisson. 1.2.3. Continuous models: Uniform, Exponential, Normal, T-student, Chi-squared, F-Snedcor. 1.2.4. Deterministic functions of random variables: Analytical results (Finite, Asymptotic) and Monte-Carlo simulation.

2. INFERENTIAL STATISTICS. 2.1. Obj. and basic concepts (Population, Sample, Statistics). 2.2. Estimation of parameters through confidence intervals: Sample estimators (Concept, Generation, Fulcrum variable, Common estimators, Point estimation), Confidence intervals (Fulcrum variable and General meth.). 2.3. Tests of hypotheses: Parametrical (General meth.) and Non-parametrical (Test of Chi-squared).

Head Lecturer(s)

Nelson Miguel Lopes Soares

Assessment Methods

Assessment
The evaluation systems based on two Midterm or a Final Examination are independent. The resolution of an extra problem is required to achieve a grade higher than 18/20: 100.0%

Bibliography

Probabilidades e Estatística para Engenharia (Probability and Statistics, In Portuguese), Jorge André (Ed. LIDEL - Edições Técnicas, 2008).

Material complementar ao livro-base: Errata, Soluções dos Problemas por Resolver (corrigidas), Resumos (material de consulta na avaliação), Tabelas (material de consulta na avaliação), Bibliografia complementar comentada, Provas de avaliação dos dois últimos anos (enunciados e correcções de referência).

Complementary material to the main bibliography: Errors list, Solutions of problems that are not solved, Comprehensive summaries of chapters (allowed the use in examinations), Tables (idem), Complementary bibliography commented, Examinations of the two previous years (questions and reference answers).