The <Chernoff bound> and part (b) give
$$
\mathbb P(f(X)\geq t)
\leq e^{-\lambda_*t}F(\lambda_*)
\leq3e^{-t/\sqrt{C_P(X)}}.
$$
Apply the same argument to $-f$ and use the <union bound> to obtain
$$
\mathbb P(|f(X)|\geq t)
\leq6e^{-t/\sqrt{C_P(X)}}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 208 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-208/2/c/solution