Correct answer: (A) U−V has a distribution symmetric about zero.; (C) The distribution of U/V does not depend on λ.
Explanation
Exchangeability gives U−V equal in law to V−U,proving A. Write U=U₀/λ,V=V₀/λ with iid Gamma(2,rate 1). Their product scales by λ⁻²,whereas their ratio cancels λ,proving C. The positive ratio has unbounded support and cannot be additively symmetric about 1; reciprocal symmetry is different. **A,C**.
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