Strong form of Han's entropy inequality

The strong form

(n - 1) \sum_{i} H (X^{(i)}) \geq n (n - 2) H (X_{1 : n}) + \sum_{i} H (X_{i})

follows by iterating entropy submodularity.

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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 208 / 2 / e / Solution

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