Description

1. Foundations of Probability Theory

2. Random Variables

3. Distribution and Density Functions

4. Functions and Sequences of Random Variables

5. Expectation. Conditional Expected

6. Characteristic Functions and Moment Generating Functions

7. Ordered Statistics

8. Multivariate normal distribution

9. Elements of Random  Processes

10. Limit Theorems

11. Simulation (using numerical Python)

Finalité

The primary objective of this course is to provide mathematical background and sufficient experience so that the student can understand sentences in the language of probability theory, as well as solve probabilistic problems in Telecommunications Engineering programs and applied science. Broad range of topics, such as random vectors, random sequences, convergence of random sequences, random processes and correlation are introduced.

Compétences visées

Upon completion of the subject, students will be able to understand:

1. The concepts surrounding probability and random processes such as the sample space, conditional probability, total probability, Bayes theorem, and independence.


2. One Random Variable and One Function of One Random Variable.


3. One function of two random variables, two functions of two random variables, moments, covariance and correlation, joint characteristic functions, conditional distributions and moments and minimum mean-square-error (MSE) estimation.


4. Sequences of Random Variables. Distributions and densities, independence, M functions of M random variables, covariance and correlation matrices and joint characteristic functions.


5. Limit Theorems. The Law of Large Numbers. The Central Limit Theorem


6. Random process. Stationarity : strict sense and wide sense. Ergodicity. Poisson Processes. Markov Processes.


7. Students will be able to understand the applications and practical issues such as the numerical simulation of random phenomena using  python.

Description des modalités d'évaluation

Validation will be done through final exam and projects

Public

Bachelor Mathematics level