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How to prove relationship between mutual information and differential entropy?

I need to prove that mutual information given by $$I(X;Y)=\int_{x,y}f(x,y) \log_2 \left( \frac{\left (f(x,y)\right)}{f(x) f(y)}\right) \, dx \, dy$$ is equivalent to $I(X;Y)=H(Y) - H(Y|X)$ I am proc …
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