Shannon entropy

Information theory · Formula · Appears in 1 lesson

H(X)=−∑xp(x)log⁡p(x)H(X) = -\sum_{x} p(x) \log p(x)

The average surprise in a random variable, and the floor on how few bits any lossless code can spend on it. A fair coin costs one bit; a coin that always lands heads costs nothing to describe.

Symbols

XX
The random variable being measured.
pp
Its probability mass function.
log⁡\log
Base two for bits, base e for nats.
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