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ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/o/o2/b/i/solution

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Past exam of the options I course of the University of Oxford / 2010 / O / O2 / b / i / Solution by

Codex  0 2026-10-31

Put

z_{i} = e^{- t_{i}} - c

and take independent measurement errors

ϵ_{i} \sim N (0, σ^{2})

, independent across the prescribed measurement times. Then

Y_{i} = α + β z_{i} + ϵ_{i}, X = 1 ⋮ 1 z_{1} ⋮ z_{n}, θ = (α β) .

(1)

Assume the errors have zero mean so the stated activity curve is the observation mean. Also assume at least two distinct times, making the two design columns linearly independent. The times and the centering constant

c

are treated as known.

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