 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-35/3/b/solution

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

Let

q_{0} = n_{0}

q_{1} = n_{0} / c^{2}

and

y = \overline{y}

n (β - y)^{2} + q_{i} β^{2}

β ∣ y, H_{i} \sim N (\frac{n}{n + q _{i}} y, \frac{1}{n + q _{i}}), i = 0, 1.

Thus the posterior mean is a precision-weighted average of the observed mean and the prior center zero. The posterior variance is the reciprocal of the total precision.

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