 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-47/6/b/iv/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

z^{(t)} = \frac{2 ( 125 )}{2 + 0.5} = 100, y_{3}^{(t)} = 125 - 100 = 25.

Applying the M-step maximum-likelihood estimator to the filled counts gives

θ^{(t + 1)} = \frac{34 + 25}{38 + 34 + 25} = \frac{59}{97} \approx 0.6082474227.

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