TOPICS COVERED :

1. Introduction to probability. Frequency definition, joint, conditional and total probabilities. Bayes theorem. Combinatorics, binomial and Poisson laws.

2. Random variables. Probability distribution and density functions. Conditional and joint distributions.

3. Functions of random variables.

4. Averages. Expectation and conditional expectation. Moments. Characteristic function.

5. Vector random variables. Joint distributions. Expectations and covariances. Multidimensional Gaussian law.

6. Estimation and detection. Parameter estimation, least squares, maximum likelihood. Confidence intervals, hypothesis testing.

7. Random sequences. Discrete-time systems, propagation of random sequences. Laws of large numbers.

8. Random processes. Classification. Linear systems with random inputs.

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