The same one-sided proxy $V^+\leq1$ lets <Talagrand's one-sided bounded differences inequality> control the opposite deviation:
$$
\mathbb P(Z-\mathbb EZ\leq-t)\leq e^{-t^2/2}.
$$
The variance estimate in part b verifies the finite-variance hypothesis in formulations of Talagrand's inequality that state it explicitly.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 208 / 4 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-208/4/c/ii/solution