 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2025/paper-1/3/g/solution

After subtracting the same training sample mean, E has vector

e = (1, - 1, 0)^{T}

(0, 2)

. The difference from D lies entirely along the first principal component. Its Euclidean distance in the retained plane is

(2 + 2)^{2} + (2 - 2)^{2} = 2 + 2 ≃ 3.4142 .

The new point must use the original centring and loadings; recomputing them with E included would change the question.

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