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Probability Theory

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Publication date January 2004

The specific value of a noisy waveform at any instant of time is inherently unpredictable. Some values, however, tend to occur more often than others. The frequency with which each value occurs can be characterized by a probability density function. This concept and other related probabilistic concepts are presented in this chapter to provide a theoretical framework for subsequent discussions. Readers desiring a more detailed and rigorous exposition should consult the references recommended at the end of the chapter.

Chapter Contents:

• 3.1 Introduction
• 3.2 Definition of Probability
• 3.3 Sample Space
• 3.4 Independent Events
• 3.5 Conditional Probability
• 3.6 Random Variables
• 3.7 Probability Distribution and Probability Density Functions
• 3.8 Joint Probability Distribution and Density Functions
• 3.9 Sums of Random Variables
• 3.10 Transformations of Random Variables
• 3.11 Statistical Averages
• 3.12 Characteristic Functions
• 3.13 The Gaussian (Normal) Distribution and the Central Limit Theorem
• 3.14 The Multidimensional Gaussian (Normal) Distribution
• 3.15 Summary
• Problems
• Reference
• Recommended Bibliography

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