1. The problem statement, all variables and given/known data I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y. 2. Relevant equations 3. The attempt at a solution X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with this product.