Under the null, $\varepsilon_1$ and $\xi_1$ have <conditional independence> given $z_1$. The <law of total expectation> gives
$$
\mathbb E(\varepsilon_1^2\xi_1^2)
=\mathbb E\!\left[
\mathbb E(\varepsilon_1^2\mid z_1)
\mathbb E(\xi_1^2\mid z_1)
\right]
\leq C^2.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 205 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-205/3/a/solution