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Mutual information $I(X;Y)$ represents the reduction in uncertainty about $X$ after observing $Y$. $H(X)$ is the initial uncertainty about $X$, and $H(X|Y)$ is the remaining uncertainty after $Y$ is known.

Conditions: $X$ and $Y$ are random variables.; $H(X)$ and $H(X|Y)$ use the same unit system.

Mutual information $I(X;Y)$ represents the reduction in uncertainty about $X$ after observing $Y$. $H(X)$ is the initial uncertainty about $X$, and $H(X|Y)$ is the remaining uncertainty after $Y$ is known.

Conditions: $X$ and $Y$ are random variables.; $H(X)$ and $H(X|Y)$ use the same unit system.