Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 4 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 4 / d / Solution

{c}

For fixed exposures $x_i\geq0$, a Poisson exposure model takes independent observations
$$
Y_i\sim\operatorname{Poisson}(\theta x_i).
$$
It has mean and variance $\theta x_i$ and is therefore heteroscedastic when the exposures differ.


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