Q21Single correct3 Marks16 Mar 2025Let (X,Y)∼Uniform(D)(X,Y)\sim\mathrm{Uniform}(D)(X,Y)∼Uniform(D) where D={(x,y):x+y<2,x>0,y>0}D=\{(x,y):x+y<2,x>0,y>0\}D={(x,y):x+y<2,x>0,y>0}. What is the marginal density function of XXX?AfX(x)={12(2−x), 0<x<2; 0 otherwise}f_X(x)=\{\frac12(2-x),\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={21(2−x), 0<x<2; 0 otherwise}BfX(x)={12(1−x), 0<x<2; 0 otherwise}f_X(x)=\{\frac12(1-x),\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={21(1−x), 0<x<2; 0 otherwise}CfX(x)={2−x, 0<x<2; 0 otherwise}f_X(x)=\{2-x,\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={2−x, 0<x<2; 0 otherwise}DfX(x)={1, 0<x<2; 0 otherwise}f_X(x)=\{1,\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={1, 0<x<2; 0 otherwise}
