 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-60/2/ii/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

The error indicator is a Bernoulli random variable with probabilities

P (Z = 1) = p_{e}

and

P (Z = 0) = 1 - p_{e}

H (Z) = h (p_{e}) = - p_{e} lo g_{2} p_{e} - (1 - p_{e}) lo g_{2} (1 - p_{e}) .

Use

0 lo g_{2} 0 = 0

, so this expression also covers error probabilities zero and one.

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