 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-219/3/c/solution

Convolving the population and measurement distributions gives

D_{s} ∣ M_{0}, τ^{2} \sim N (M_{0}, τ^{2} + σ^{2}) .

Put

V = τ^{2} + σ^{2}

. With a flat prior on

M_{0}

M_{0} ∣ τ^{2}, D \sim N (\overset{ˉ}{D}, V / N) .

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