2024
Probability and Statistics
Name: Probability and Statistics
Code: MAT02354L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
To provide concepts and methods of probability theory and statistical inference, looking for the interpretation and analysis of data and making statistical inference to support decision making.
Sustainable Development Goals
Learning Goals
Outcomes:
To provide fundamental concepts and methods of probability theory and statistical inference;
To know the main probability distributions;
To understand the importance of ordinary and centered moments, a well as the moments and probability generating functions.
To know point estimation methods;
To know how to build confidence intervals and hypothesis tests for one and two populations;
To know how to validate the assumptions underlying statistical inference for one and two populations and know how to use non-parametric alternatives when they are not valid.
Competences:
Ability to critically select and apply appropriate methods in order to draw conclusions that assist decision-making;
Ability to critically interpret results;
Ability to learn autonomously and adapt to new situations;
Develop teamwork skills.
To provide fundamental concepts and methods of probability theory and statistical inference;
To know the main probability distributions;
To understand the importance of ordinary and centered moments, a well as the moments and probability generating functions.
To know point estimation methods;
To know how to build confidence intervals and hypothesis tests for one and two populations;
To know how to validate the assumptions underlying statistical inference for one and two populations and know how to use non-parametric alternatives when they are not valid.
Competences:
Ability to critically select and apply appropriate methods in order to draw conclusions that assist decision-making;
Ability to critically interpret results;
Ability to learn autonomously and adapt to new situations;
Develop teamwork skills.
Contents
Probabilities and Conditional Probabilities.
One and two-dimensional random variables (discrete and continuous).
Moments. Moment and probability generating functions.
Main probability distributions.
Point estimation (moment and maximum likelihood estimation methods and properties of estimators).
Confidence intervals for one and two populations.
Hypothesis tests for one and two populations.
Nonparametric alternatives for one and two populations.
One and two-dimensional random variables (discrete and continuous).
Moments. Moment and probability generating functions.
Main probability distributions.
Point estimation (moment and maximum likelihood estimation methods and properties of estimators).
Confidence intervals for one and two populations.
Hypothesis tests for one and two populations.
Nonparametric alternatives for one and two populations.
Teaching Methods
The teaching sessions are theoretical-practical, combining the concepts with their application to concrete cases in the area of Economics and Management. Sessions include the resolution of practical exercises using real data whenever possible, and students actively participate in their resolution and / or discussion. In addition to the sessions, students are encouraged to solve practical exercises on their own in order to develop autonomy. There will be some classes in computer lab with the use of software R, also being analyzed and interpreted, in non-laboratory classes, outputs for problems solving with real data.
Assessment
In continuous assessment, students carry out a practical work in groups, using necessarily the R software (15%) and two frequencies (the first with a weight of 40% and the second with a weight of 45%).
The final grade is the result of the weighted average between the work and the two frequencies.
The final assessment regime consists of a written exam in the regular period and a written exam in the appeal period.
The student is Approved when the final classification equals or exceeds 10 values.
The final grade is the result of the weighted average between the work and the two frequencies.
The final assessment regime consists of a written exam in the regular period and a written exam in the appeal period.
The student is Approved when the final classification equals or exceeds 10 values.
Teaching Staff (2023/2024 )
- Gonçalo João Costa Jacinto
- Paulo de Jesus Infante dos Santos [responsible]
