Probability and Statistics
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2022/2023 - 1S
Cycles of Study/Courses
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:
- understand the concepts involved in a statistical study and be aware of the various problems that arise in each particular study;
- correctly identify and apply the learnt techniques from Descritive Statistics, used to summarize data, and to interpret them;
- master the the probability concepts and calculus approached in the curricular unit;
- be able to characterize random variables/vectors and to identify the correspondent probability distributions;
- 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. independent random variables. Binomial, exponencial, normal distributions. The Central Limit Theorem.
3. Descriptive Statistics: fundamental concepts, types of observations and measurement scales, techniques for data summarization, using software R
4. 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.
Hipothesis tests.
Mandatory literature
Murteira Bento;
Introdução à estatística. ISBN: 972-773-116-3
Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers, 7th Edition, John Wiley & Sons, 2018. ISBN: 978-1-119-40036-3
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
Teaching methods and learning activities
Theoretical lectures with exposition of the course contents. The lecture notes are previously made available on the web page of the curricular unit.
Practical classes with solution of exercises by the students and support in clarifying theoretical and/or practical problems by the lecturer.
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 |
106,00 |
Frequência das aulas |
56,00 |
Total: |
162,00 |
Eligibility for exams
Without restrictions.
Calculation formula of final grade
1. In the first call the final mark will be the sum of the scores obtained in two assessments:
Assessment 1: with a total of 8 points, will take place on a date to be settled with students.
Assessment 2: with a total of 12 points, will take place during the period settled for the conclusion of distributed evaluation.
2. In the second call, the final mark will be obtained in an exam with a total of 20 points.
This exam will be divided into two parts, allowing the students which have not yet been approved in the course (and only these students) to substitute the score in any of the two parts by the score obtained in the corresponding assessment.
The students will be sucessful in the curricular unit once the final grade (obtained in the final examination) is greater than or equal to 9.5.
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
Exams under speacial conditions will consist of a written test or oral test which can be preceded by an oral eliminatory exam.
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.