Entropy of a random variable indicates how hard to predict the value of the variable or the uncertainty of the variable. It’s also called “expected surprisal”.

$$\begin{align} H(x) &= -\int p(x)\log p(x)\mathrm{d}x \\ &= -\operatorname{E}\left[ \log p(x)\right] \end{align}$$

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Illustration: Entropy of a coin flip

Reference

Entropy: https://en.wikipedia.org/wiki/Entropy