 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/31k/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

ε_{1}, \dots, ε_{n}

be independent Rademacher signs. For the set of evaluation vectors

F (z_{1 : n}) = {(f (z_{1}), \dots, f (z_{n})) : f \in F},

R (F (z_{1 : n})) = E_{ε} [sup_{f \in F} \frac{1}{n} \sum_{i = 1}^{n} ε_{i} f (z_{i})] .

For an independent sample

Z_{1}, \dots, Z_{n}

R_{n} (F) = E_{Z_{1 : n}} R (F (Z_{1 : n})) .

 New to topics? Read the docs here!