Probability and Statistics

Code:

M2016

Acronym:

M2016

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 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	54	Plano de estudos a partir de 2014	2	-	6	56	162
MI:ERS	100	Plano Oficial desde ano letivo 2014	2	-	6	56	162

Teaching language

Portuguese

Objectives

Introductory course in Probability and Statistics: acquisition of basic concepts and application to real situations.
Particular attention will be paid to the presentation and understanding of the concepts, keeping the mathematical treatment at a median level.

Learning outcomes and competences

On completing this curricular unit, the student is expected to:

1. understand the concepts involved in a statistical study and be aware of the various problems that arise in each particular study;
2. correctly identify and apply the learnt techniques from Descritive Statistics, used to summarize data, and to interpret them;
3. master the the probability concepts and calculus approached in the curricular unit;
4. be able to characterize random variables/vectors and to identify the correspondent probability distributions;
5. be able to make simple statistical inferences on basic population parameter,s from point and interval estimation techniques.

Working method

Presencial

Program

1. Probability Theory: fundamental concepts, independence of events and conditional probability, the Bayes’ and the total probability theorems.

2. Univariate random variables: definition, probability (density) function and probability distribution function; expected value and its properties; variance and its properties.
Bivariate random variables; joint distributions; covariance and correlation; independent random variables.  

3. Some probability distributions: discrete distributions (uniform, binomial, multinomial and Poisson) and continuous distributions (uniform, normal, exponential, chi-squared and Student's t). The De Moivre-Laplace and the Central Limit Theorem.

4. Descriptive Statistics: fundamental concepts, types of observations and measurement scales, techniques for data summarization (tables, plots, measures of location and scale), outliers, Pearson's correlation coefficient. 

5. Statistical Inference: random sample, statistic, sample mean and sample proportion. 
Point estimation: properties (bias and consistency). 
Some sample distributions. Interval estimation: computation and interpretation of confidence intervals for some population parameters.

Mandatory literature

Pestana Dinis Duarte; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9
A. Rita Gaio; Apontamentos da uc

Complementary Bibliography

Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers, John Wiley & Sons, 2003. ISBN: 0-471-20454-4
Murteira Bento; Introdução à estatística. ISBN: 972-773-116-3

Teaching methods and learning activities

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Calculation formula of final grade

Final classification obtained by a distributed assessment:
Final mark = 0.4xT1 + 0.6xT2
where
T1 = the first test rating (0-20)
T2 = the second test rating (0-20)
T1 >= 8.0    and    T2 >= 8.0 


Final classification obtained by examination:
mark of the final exam.




Students with a score greater than or equal to 17.5 values in the final exam must make a complementary written or oral exam in order to obtain a final score greater than or equal to 18 values.

Examinations or Special Assignments