Mutual information

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Information theory
Entropy Differential entropy Conditional entropy Joint entropy Mutual information Conditional mutual information Entropy rate
Asymptotic equipartition property Rate–distortion theory
Shannon's source coding theorem Noisy-channel coding theorem
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Mutual information measures how much more is known about one random value when given another. For example, knowing the temperature of a random day of the year will not reveal what month it is, but it will give some hint. In the same way, knowing what month it is will not reveal the exact temperature, but will make certain temperatures more or less likely. These hints or changes in likelihood are explained and measured with mutual information.