Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 17H / a / Solution

For $S_r=\sum_i x_i^r$, unweighted least squares through the origin and maximum likelihood give
$$
\widehat\theta_{LS}=\frac{\sum_i x_iY_i}{S_2},
\qquad
\widehat\theta_{MLE}=\frac{\sum_iY_i}{S_1}.
$$
Both estimators are unbiased.


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