 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2010/m/m4/a/ii/solution

Integrate the joint density in

u

. Symmetry gives

f (- u) g (- uv) = f (u) g (uv)

∣ u ∣ f (u) g (uv)

is even. Hence

f_{V} (v) = \int_{R} ∣ u ∣ f (u) g (uv) d u = 2 \int_{0}^{\infty} u f (u) g (uv) d u .

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