Q3Single correct3 Marks16 Mar 2025Let X∼Uniform{1,2}X\sim\mathrm{Uniform}\{1,2\}X∼Uniform{1,2} be discrete. Let (Y∣X=1)∼Exp(1)(Y\mid X=1)\sim\mathrm{Exp}(1)(Y∣X=1)∼Exp(1) and (Y∣X=2)∼Exp(2)(Y\mid X=2)\sim\mathrm{Exp}(2)(Y∣X=2)∼Exp(2). Find the distribution of YYY.AfY(y)=12e−y+2e−2y, y>0f_Y(y)=\frac12e^{-y}+2e^{-2y},\ y>0fY(y)=21e−y+2e−2y, y>0BfY(y)=12e−y+e−2y, y>0f_Y(y)=\frac12e^{-y}+e^{-2y},\ y>0fY(y)=21e−y+e−2y, y>0CfY(y)=12(e−y+e−2y), y>0f_Y(y)=\frac12(e^{-y}+e^{-2y}),\ y>0fY(y)=21(e−y+e−2y), y>0DfY(y)=12(e−2y+2e−y), y>0f_Y(y)=\frac12(e^{-2y}+2e^{-y}),\ y>0fY(y)=21(e−2y+2e−y), y>0
