 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-2/9f/a/solution

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

Because

U

and

V

are bounded, their exponential series may be integrated term by term for every real

t

M_{U} (t) = E [e^{t U}] = \sum_{j = 0}^{\infty} \frac{t ^{j}}{j !} E [U^{j}],

and similarly for

V

. Equality of every moment gives equality term by term, so

M_{U} (t) = M_{V} (t) for every t \in R .

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