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I don't know if $N(X)$ has a name or has any applicability in AI, but I can comment on how this function varies as the $H(X)$ based on your equation $$N(X) = \dfrac{1}{2^{H(X)}}$$ which looks correct to me (just apply the $\log_2$ to both sides). In the case of a Bernoulli random variable (which is a categorical r.v. that can take 2 values, $0$ or $1$, which ...

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