QuestionLet X∼Uniform{1,2}X\sim\mathrm{Uniform}\{1,2\} be discrete. Let (Y∣X=1)∼Exp(1)(Y\mid X=1)\sim\mathrm{Exp}(1) and (Y∣X=2)∼Exp(2)(Y\mid X=2)\sim\mathrm{Exp}(2). Find the distribution of YY.
