Utilizing heuristics to present some fundamentals of probability theory, this book discusses the ideas and concepts common to all random problems. It provides readers with the elementary basis of calculation of probabilities so that it can solve the vast majority of problems it encounters in signal processing, then brings the reader to a more precise knowledge of the theory of measure and Lebesgue integration from the limitations of the tools proposed.
Part
1. Random and Formalism
1. Lebesgue integral of real functions
2. Notion of random experience
3. Elementary discrete probabilistic
models
4. Non-elementary discrete probabilistic models
5.
Probabilisables spaces and probabilistic Part
2. Probabilistic space and
random variables
6. Real random variables
7. Real discrete random
variables and absolutely continuous
8. Couple of real expenditures random
variables
9. Esperance of random variables
10. Variance and standard
deviation
11. Transfer theorem, moments and characteristic function
12.
Examples of laws
13. Independence and decorrelation
14. conditioning
15. random vectors Part
3. Conditioning and Independence Appendices
