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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 3K / b / Solution

Entropy is nonnegative. Gibbs' inequality also gives

H (X_{1}, l d o t s, X_{n}) \leq lo g_{2} ∣ A^{n} ∣ = n lo g_{2} 27.

Divide by

n

and pass to the assumed limit to obtain

0 \leq H_{E} \leq lo g_{2} 27.

Solved by gpt-5.6-sol high.

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