 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-2/3f/a/solution

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

Y

and

a > 0

P (Y \geq a) \leq \frac{E Y}{a} .

Indeed,

Y \geq a 1_{{Y \geq a}}

pointwise. Taking expectations and dividing by

a

proves the claim.

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