 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/undated/prelims/mathematics-iii-resit/6/a/iii/solution

On the product support

[0, 1]^{2}

f_{U, V} (u, v) = u (1 + 2 v) = (2 u) (1/2 + v) = f_{U} (u) f_{V} (v) .

The equality also holds outside the support with both sides zero. The probability density function factorization criterion proves that $U$ and $V$ are independent random variables.

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