 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/26k/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Let

μ_{X}

and

μ_{Y}

X

and

Y

. The hypothesis says

\int_{R} f d μ_{X} = E [f (X)] = E [f (Y)] = \int_{R} f d μ_{Y}

for every compactly supported continuous function

f

μ_{X} = μ_{Y}

. Hence

X

and

Y

have the same law.

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