Course: 2020/2021

Probability

(18269)

ObjectivesFurther information on this link

SPECIFIC SKILLS
Students will acquire knowledge and skills necessary to:
1. Knowing the theoretical foundations and calculus rules of Probability Theory.
3. Resolution of problems of Probabilistic Nature.
GENERAL SKILLS
Students will be able to:
1. Develop their ability to think analytically
1. Become familiar with a statistical software
2. Establish a framework to solve problems
3. Develop their interactive skills
4. Enhance their critical thinking
5. Improve their learning skills and communication

Description of contents: programme

1. Probability and random phenomena.
1.1 Random phenomena, sample space, events.
1.2 Axioms of Probability and elementary properties.
1.3 Conditional probability and independence.
1.4 Total probability rule and Bayes¿ formula.
2. Random variables.
2.1 Definition of random variable.
2.2 Expectation, characteristic features, and moments of a random variable.
2.3 Discrete probability models.
2.4 Continuous probability models.
2.5 Transformations of random variables.
3. Jointly distributed random variables
3.1 Definition of random vector, joint, marginal, and conditional distributions.
3.2 Independent random variables.
3.3 Some multivariate distribution models.
3.4 Transformations.
4. Properties of the expectation.
4.1 Expectations of transformation of random variables.
4.2 Covariance, variance of sums, and correlation.
4.3 Conditional expectation.
4.4 Moment generating functions.
5. Limit Theorems.
5.1 Chebyshev¿s inequality.
5.2 Convergence in probability, the Weak Law of Large Numbers.
5.3 Almost sure convergence, the Strong Law of Large Numbers.
5.4 Convergence in distribution, the Central Limit Theorem.

Learning activities and methodology

- Lectures: introducing the theoretical concepts and developments with examples, 2.2 ECTS
- Problem solving sessions: 2.2 ECTS
- Computer (practical) sessions: 0.6 ECTS
- Evaluation sessions (continuous evaluation and final exam): 1 ECTS

Assessment System

- % end-of-term-examination 40
- % of continuous assessment (assigments, laboratory, practicals...) 60

Basic Bibliography

- Jeffrey S. Rosenthal . A First Look at Rigorous Probability Theory. .World Scientific Publishing. 2006
- Sheldon M. Ross. A First Course in Probability. Prentice Hall. 2010