Shannoninformációtartalmat

Shannoninformációtartalom, often translated as Shannon information content or surprisal, is a concept introduced by Claude Shannon in his seminal work on information theory. It quantifies the amount of information contained in a single event or outcome of a random variable. The information content of an event is inversely proportional to its probability; a less probable event carries more information because it is more surprising.

Mathematically, the Shannon information content of an event with probability P is defined as -log₂(P). The base-2 logarithm is used so that the unit of information is the bit. If an event has a probability of 1, its information content is 0, as it provides no new information. Conversely, an event with a probability of 0.5 has an information content of 1 bit, meaning it resolves as much uncertainty as a fair coin flip.

This concept is fundamental to understanding various aspects of information theory, including entropy, channel capacity, and data compression. Entropy, for instance, is the expected value of the Shannon information content over all possible outcomes of a random variable. It represents the average amount of information per outcome. Shannoninformációtartalom provides a rigorous way to measure the "unexpectedness" or "informativeness" of individual occurrences in a probabilistic setting.