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Embedded SystemsFPGAElectronics

Spectral Audio Signal Processing
    Beginning Statistical Signal Processing
       Random Variables & Stochastic Processes
          Independent Events

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Independent Events

Two probabilistic events $ H_1$ and $ H_2$ are said to be independent if the probability of $ H_1$ and $ H_2$ occurring together equals the product of the probabilities of $ H_1$ and $ H_2$ individually, i.e.,

$\displaystyle p(H_1 H_2) = p(H_1)(H_2) $

where $ p(H_1 H_2)$ denotes the probability of $ H_1$ and $ H_2$ occurring together.



Example: Successive coin tosses are normally independent. Therefore, the probability of getting heads twice in a row is given by

$\displaystyle p(H H) = p(H)p(H) = \frac{1}{2}\cdot\frac{1}{2} = \frac{1}{4}. $

Previous: Probability Distribution
Next: Random Variable

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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