Q17Comprehension2 Marks3 Aug 2025PassageLet X∼Uniform{1,2}X\sim\mathrm{Uniform}\{1,2\}X∼Uniform{1,2} be discrete. Let Y∣X=1∼Exponential(1)Y\mid X=1\sim\mathrm{Exponential}(1)Y∣X=1∼Exponential(1) and Y∣X=2∼Exponential(2)Y\mid X=2\sim\mathrm{Exponential}(2)Y∣X=2∼Exponential(2). Based on the above data, answer the subquestions.What is the marginal distribution of YYY?A12(e−y+e−2y); y≥0\frac12(e^{-y}+e^{-2y});\ y\ge021(e−y+e−2y); y≥0B12e−y+e−2y; y≥0\frac12e^{-y}+e^{-2y};\ y\ge021e−y+e−2y; y≥0Ce−y+e−2y; y≥0e^{-y}+e^{-2y};\ y\ge0e−y+e−2y; y≥0D12e−y+2e−2y; y≥0\frac12e^{-y}+2e^{-2y};\ y\ge021e−y+2e−2y; y≥0
