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Joint entropy

Information theory · Formula · Not yet linked from a lesson

H(X,Y)=−∑x,yp(x,y)log⁡p(x,y)H(X, Y) = -\sum_{x, y} p(x, y) \log p(x, y)

The total uncertainty in two variables considered together. It is never more than the sum of the separate entropies, and the shortfall is exactly how much the two share.

Symbols

p(x,y)p(x, y)
The joint probability of both outcomes.
XX
The first random variable.
YY
The second random variable.
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