Probability and Statistics

Code	16147
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Assist to calculus I and calculus II.
Learning outcomes	Obtain essential knowledge of Probability and Statistical Inference, essential to the future learning of more advanced concepts that arise in the course of academic and/or professional training. At the end of the course unit the learner is expected to be able to: 1 - identify engineering problems likely to be solved using methodologies of Probability and Statistical Inference; 2 - build probabilistic models adequate to the problems; 3 - select and apply Probability and Statistical Inference methodologies to solve problems; 4 - interpret critically and communicate rigorously the results obtained.
Syllabus	0. Introduction and Brief Review of Descriptive Statistics 1. Theory of probabilities 1.1 Random experiences and happenings 1.2 Conditioned probability and independence of events 1.3 Total probability theorem and T. Bayes 2. Real random variables and probability distributions 2.1 Distribution Function. properties 2.2 Discrete and continuous random variables 2.3 Parameters of a random variable 2.4 Random variables of two or more dimensions. properties 3. Theoretical models: discrete and continuous 3.1 Central Limit Theorem and its applications 3.2 De Moivre–Laplace Theorem 4 Point and interval estimation 4.1 Estimators. properties 5 Hypothesis Testing 5.1 Null hypothesis versus alternative hypothesis, p-value 6. Simple linear regression model 6.1 Least squares estimators 6.2 determination and correlation coefficient
Main Bibliography	Bibliography: -Gonçalves, E., Nogueira, E. e Rosa, A.C. (2016). Probabilidades e Estatística para Ciências e Tecnologia. Conceitos e exercícios resolvidos. Almedina. - Montgomery, D., e Runger, G. (2011). Applied statistics and probability for engineers, 5th Edt, John Wiley & Sons. -Ross, S. (2009). Introduction to probability and statistics for engineers and scientists. Amsterdam Elsevier. - Guimarães, R. e Cabral, J. (1997). Estatística. McGraw-Hill. - Murteira, B., Ribeiro, C., Andrade e Silva, J. e Pimenta, C. (2002). Introdução à Estatística. McGraw-Hill. - Pestana, D. ,Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian. Lisboa. complementary bibliography - Mood, A., Graybill, F., and Boes, D. (1985). Introduction to the Theory of Statistics. 3rd edition. International Student Edition. - Draper, N. R., Smith, H. (1998), Applied Regression Analysis, John Wiley and Sons, 3ª Edição.
Teaching Methodologies and Assessment Criteria	The measurement of knowledge and skills acquired by students during teaching-learning is done through two frequencies (classified from 0 to 20 values) with a weighting of 0.5. The final teaching-learning classification (0 to 20 values) is calculated as follows: CEA=0.5F_1+0.5F_2. F_1- 1st test; F_2- 2nd test. First Test - November 7; Second Test- January 5. Exemption from the final exam is granted when the final teaching-learning classification is equal to or greater than 9.5 values and attendance exceeds 40%. The “FREQUENCY” classification is awarded when the final teaching–learning grade is between 6.0 (inclusive) and 9.5 (exclusive), and it is also granted to working students and finalists. In cases where a student attains a grade exceeding 17 and wishes to retain that classification, the student is required to complete a supplementary assessment to maintain it. Nevertheless, the grade of 17 is assured.
Language	Portuguese. Tutorial support is available in English.