Q52Single correct3 Marks3 Dec 2024Let (X,Y)∼Uniform(D)(X,Y)\sim \mathrm{Uniform}(D)(X,Y)∼Uniform(D), where D={(x,y):x+y<3, x>0, y>0}D=\{(x,y):x+y<3,\ x>0,\ y>0\}D={(x,y):x+y<3, x>0, y>0}. What is the marginal density function of fX(x)f_X(x)fX(x)?AfX(x)=29(3−x)f_X(x)=\frac{2}{9}(3-x)fX(x)=92(3−x), 0<x<30<x<30<x<3; 000 otherwiseBfX(x)=32(3−x)f_X(x)=\frac{3}{2}(3-x)fX(x)=23(3−x), 0<x<30<x<30<x<3; 000 otherwiseCfX(x)=92(3−x)f_X(x)=\frac{9}{2}(3-x)fX(x)=29(3−x), 0<x<30<x<30<x<3; 000 otherwiseDfX(x)=2(3−x)f_X(x)=2(3-x)fX(x)=2(3−x), 0<x<30<x<30<x<3; 000 otherwise
