Probability and Statistics

Code:

M2016

Acronym:

M2016

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Computer Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:CC	40	Plano de estudos a partir de 2014	2	-	6	56	162
MI:ERS	76	Plano Oficial desde ano letivo 2014	2	-	6	56	162

Teaching language

Portuguese

Objectives

To introduce the fundamental concepts, principles and methods of statistics. Emphasis is given to the understanding of the concepts and to the critical application of the methods.

Learning outcomes and competences

It is intended that the student

. Understand the fundamental concepts of probability theory and know how to calculate probabilities associated with the events being studied;

. Be able to identify the techniques of descriptive statistics appropriate to organize and summarize a data set, and how to apply them;

. Be able to characterize random variables and identify their probability distributions;

· Be able to apply adequate point and interval estimation methods to infer about the characteristics of a population based on a sample and to interpret the obtained results;

. Understand the general procedures for applying a hypothesis test;

. Become familiar with the software R for solving statistical problems.

Working method

Presencial

Program

1. Brief introduction to the u.c. objectives and methodology of statistics. 

2. Probability theory: basic concepts, operations between events, counting methods (review of the combinatorial calculus), interpretations of probability, independence of events and conditional probability, Bayes' theorem and the total probability theorem. 

3. Random variables: definition of random variable, probability function, probability density function and distribution function. Expected value, variance and their properties; multidimensional variables, independence and conditioning. 

4. Some probability distributions: discrete distributions (binomial, geometric, hypergeometric and Poisson) and continuous (uniform, normal, exponential, chi-square and t-student); de Moivre-Laplace and the Central Limit theorems. 

5. Descriptive Statistics: definition of a statistic, types of observations and measurement scales; techniques for summarizing data (tables, graphs, measures of location and dispersion), outlier definition and the concept of correlation. 

6. Techniques of statistical inference: point estimation (main concepts and properties of the estimators), interval estimation and introduction to hypothesis testing. 

7. Solution of problems using the software R. 

Mandatory literature

000101723. ISBN: 978-84-481-6099-2
000038821

Teaching methods and learning activities

Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts.
The practical classes are accompanied by exercise sheets relating to each of the programmatic sections; some sections are also accompanied by the use of software R in practical classes with computer.

Software

Software R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Calculation formula of final grade

Students may take two intermediate tests throughout the semester and also a final exam. The minimum score in each test is 7 (out of 20) and the tests provide exemption from the final exam, if, moreover, the mean score of the tests is at least 10. Students exempted from the final exam may still take it and, in case they want it to be graded, the mean score of the tests is replaced by the score obtained in the final exam. Students with more than 17 points must take an extra test, otherwise their final score will be 17.