Probability and Statistics

Code:

M2016

Acronym:

M2016

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2020/2021 - 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	82	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

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

À distância

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

Murteira Bento; Introdução à estatística. ISBN: 972-773-116-3

Complementary Bibliography

Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers, John Wiley & Sons, 2003. ISBN: 0-471-20454-4
Pestana Dinis Duarte; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9
Dagnelie Pierre; Estatística

Teaching methods and learning activities

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Without restrictions.

Calculation formula of final grade

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. Otherwise their final score is 17.

Examinations or Special Assignments

Classification improvement

Exam's score if less than or equal to 17. If the exam's score is greater than or equal to 17.5, a complementary assessment, oral or written, may be required, to take place in a date to fix with the students. In this case, the final grade can be 17, 18, 19 or 20 values and will only depend on on the student's performance in this complementary assessment.