 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/3h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For the binary code above, the lengths are

1, 2, 3, 5, 5, 5, 5

. Thus

\overset{ˉ}{ℓ} = .45 + 2 (.28) + 3 (.14) + 5 (.04 + .04 + .03 + .02) = 2.08.

This is optimal by Huffman coding.

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