Q31Comprehension3 Marks1 Dec 2024PassageLet (X,Y)∼Uniform(D)(X,Y)\sim\mathrm{Uniform}(D)(X,Y)∼Uniform(D) where D=[0,2]×[0,2]D=[0,2]\times[0,2]D=[0,2]×[0,2]. Based on the above data, answer the subquestions.Find the joint density function fXY(x,y)f_{XY}(x,y)fXY(x,y).AfXY(x,y)=2, 0<x<2,0<y<2; 0 otherwisef_{XY}(x,y)=2,\ 0<x<2,0<y<2;\ 0\text{ otherwise}fXY(x,y)=2, 0<x<2,0<y<2; 0 otherwiseBfXY(x,y)=1/2, 0<x<2,0<y<2; 0 otherwisef_{XY}(x,y)=1/2,\ 0<x<2,0<y<2;\ 0\text{ otherwise}fXY(x,y)=1/2, 0<x<2,0<y<2; 0 otherwiseCfXY(x,y)=1/4, 0<x<2,0<y<4; 0 otherwisef_{XY}(x,y)=1/4,\ 0<x<2,0<y<4;\ 0\text{ otherwise}fXY(x,y)=1/4, 0<x<2,0<y<4; 0 otherwiseDfXY(x,y)=1/4, 0<x<2,0<y<2; 0 otherwisef_{XY}(x,y)=1/4,\ 0<x<2,0<y<2;\ 0\text{ otherwise}fXY(x,y)=1/4, 0<x<2,0<y<2; 0 otherwise
