Probability and Statistics
Code
3645
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Luís Pedro Carneiro Ramos
Weekly hours
5
Total hours
70
Teaching language
Português
Objectives
The aim of the course is to provide students a basic knowledge of Probabilities and Statistics which are an indispensable tool for decision making under uncertainty, present in many areas in the field of Engineering. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study.
At the end of the unit students will have acquired skills that enable them:
Know and understand the basic elements of the theory and the calculus of probabilities
Describe the main probabilistic distributions of discrete and continuous variables and applies them in the description of random phenomena
Infer about population parameters based on sample distributions
Buildstatistical models, which establish a functional relationship between variables
Prerequisites
Basics of mathematical analysis, pointing out some topological notions, primitives, integrals and functions of more than one variable.
Subject matter
PROBABILITY

Random experiment; Sample space; Random event; Algebra of events
 Axioms of probability and addition rules
 Conditional probability
 Total probability rule
 Bayes theorem
 Random variable
 Distribution function
 Discrete random variable
 Probability function
 Mean value and properties
 Variance, standard variation and properties
 Continuous random variable
 density function
 Mean value, variance and standard deviation
 Chebychev inequality
 Discrete random pair
 Joint and marginal probability functions
 Covariance and properties
 Correlation coefficient and properties
 Important discrete distributions: Hipergeometric, Binomial, Poisson
 Important continuous distributions: Uniform, Exponential and Normal
 Central Limit Theorem
STATISTICS

Elementar concepts in statistic

Population, random sample and observed sample

Simple random sample

Pontual estimation

Estimators and estimatives

Desirable properties for estimators: unbiased and minimum variance estimators

Method of moments

Confidence interval estimation: elementar concepts

Confidence interval estimation for the: mean value, variance, standard deviation, proportion, difference of mean values, ratio of variances

Tests of hypotheses

Elementar concepts

Hypothesis, null hypothesis, alternative hypothesis, simple and compound hypotheses

Decision and critical region

Decision errors and probabilites

Significance level

Bilateral and unilateral tests for the: mean value, variance, standard deviation, proportion, difference of mean values, ratio of variances

Testing for godness of fit to normality: chisquare test

Randomeness test

Contingency tables: test for independence

Simple linear regression

Pontual and confidence interval estimation for the model parameters

Bilateral and unilateral tests for the model parameters

Testing the quality of the model
 Pontual and confidence interval estimation on the: mean response and new observation prediction
Bibliography
Guimarães, R.C. & Cabral, J.A.S. (2007), Estatística, McGrawHill.
Montgomery, D.C. & Runger, G.C. (2011), Applied Statistics and Probability for Engineers, John Wiley.
Pedrosa, A.C.& Gama, S.M.A. (2004), Introdução Computacional à Probabilidade e Estatística, Porto Editora.
Pestana, D.D. & Velosa, S.F. (2002) Introdução à Probabilidade e à Estatística, Fundação Calouste Gulbenkian, Lisboa.
Robalo, A. (1994), Estatística  Exercícios, vol. I, II, Edições Sílabo, Portugal.
Teaching method
Lectures and problemsolving sessions, with wide participation of students.
Evaluation method
The classes take place with an oral presentation of the subjects, followed by practical examples. Learning is complemented by solving exercises.
Frequency: Obtained with at least two thirds of attendance in classes taught in each module.
CONTINUOUS EVALUATION
The students obtain approval if the weighted average of the three tests is greater than or equal to 9.5. If a student does not attend a test, this test will come with the factor of "0 x corresponding percentage" for the final classification.
Final mark = 30%T1 + 50%T2 + 20%T3
EVALUATION BY EXAM
The evaluation by exam is valid both for grade improvement as for discipline approval. The student with a final score greater than or equal to 18.5 should carry out an oral defense of note. Otherwise, will get a final score of 18.0.
More detailed rules are available in the Portuguese version.