Q15Comprehension3 Marks3 Aug 2025PassageLet (X,Y)∼Uniform(D)(X,Y)\sim \mathrm{Uniform}(D)(X,Y)∼Uniform(D), where D={(x,y):x2+y2<4,x>0,y>0}D=\{(x,y):x^2+y^2<4,x>0,y>0\}D={(x,y):x2+y2<4,x>0,y>0}. Based on the above data, answer the given subquestions.What is the marginal density function fX(x)f_X(x)fX(x)?AfX(x)={4−x2/π, 0<x<4; 0 otherwise}f_X(x)=\{\sqrt{4-x^2}/\pi,\ 0<x<4;\ 0\text{ otherwise}\}fX(x)={4−x2/π, 0<x<4; 0 otherwise}BfX(x)={4−x2/(4π), 0<x<2; 0 otherwise}f_X(x)=\{\sqrt{4-x^2}/(4\pi),\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={4−x2/(4π), 0<x<2; 0 otherwise}CfX(x)={1−x2/π, 0<x<4; 0 otherwise}f_X(x)=\{\sqrt{1-x^2}/\pi,\ 0<x<4;\ 0\text{ otherwise}\}fX(x)={1−x2/π, 0<x<4; 0 otherwise}DfX(x)={4−x2/π, 0<x<2; 0 otherwise}f_X(x)=\{\sqrt{4-x^2}/\pi,\ 0<x<2;\ 0\text{ otherwise}\}fX(x)={4−x2/π, 0<x<2; 0 otherwise}
