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Information can be modeled as the resolution or reduction of uncertainty about a random event.
In information theory, uncertainty represents the lack of knowledge about the outcome of a random variable. Information is understood as the reduction or resolution of this uncertainty when an outcome becomes known. For example, before a fair coin is flipped, the result is uncertain and has an entropy of 1 bit; after the result is observed, the uncertainty and remaining entropy are zero. Shannon entropy provides a mathematical measure of uncertainty based on the probabilities of possible outcomes. It is calculated as the expected value of self-information, with less probable events carrying more information when they occur. Entropy is highest when all possible outcomes are equally likely and lower when one outcome is more predictable. This model supports applications such as data compression, reliable communication, statistical inference, and error correction.
Information can be modeled as the resolution or reduction of uncertainty about a random event.
Shannon entropy quantifies the average uncertainty in a probability distribution.
A rare or unexpected event conveys more information than a common or predictable event.
Entropy is maximized when all possible outcomes are equally probable.
A fair binary outcome has an entropy of 1 bit, while a known outcome has zero entropy.
The uncertainty model underlies data compression and communication through noisy channels.
A measure of limited knowledge about which outcome of a random variable will occur.
The reduction or resolution of uncertainty produced by observing an outcome.
The expected amount of uncertainty or information associated with a random variable.
The information provided by a specific outcome, calculated as the negative logarithm of its probability.
Another name for self-information, emphasizing that unlikely events are more informative.
The standard unit of information based on the base-2 logarithm, representing the uncertainty of an equally likely binary choice.
A description of the likelihood assigned to each possible outcome of a random variable.
The entropy of a two-outcome random variable, reaching one bit when both outcomes are equally likely.
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