 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/27k/b/solution

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

Let

U

[0, 1]

, and set

Z_{1} = U, Z_{2} = U .

The variables have the same law. They are not independent random variables, since

P (Z_{1} \leq \frac{1}{2}, Z_{2} \leq \frac{1}{2}) = \frac{1}{2} \neq = \frac{1}{4} = P (Z_{1} \leq \frac{1}{2}) P (Z_{2} \leq \frac{1}{2}) .

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