 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2025/paper-1/7/b/solution

The centred observations sum to zero:

\sum_{x \in C_{k}} (x - \overset{x}{ˉ}_{k}) = \sum_{x \in C_{k}} x - n_{k} \overset{x}{ˉ}_{k} = 0.

\sum_{x \in C_{k}} (x - \overset{x}{ˉ}_{k})^{T} (z - \overset{x}{ˉ}_{k}) = (\sum_{x \in C_{k}} (x - \overset{x}{ˉ}_{k}))^{T} (z - \overset{x}{ˉ}_{k}) = 0.

This cancellation holds for every

z

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