Q36Comprehension3 Marks4 Aug 2024PassageLet XXX and YYY have joint density fXY(x,y)=15x2y2f_{XY}(x,y)=15x^2y^2fXY(x,y)=15x2y2 for x≥0,y≥0,x+y≤1x\ge0,y\ge0,x+y\le1x≥0,y≥0,x+y≤1, and 000 otherwise. Based on the above data, answer the subquestions.Find the conditional distribution fY∣X(y∣x)f_{Y|X}(y|x)fY∣X(y∣x).AfY∣X(y∣x)=3y2(1−y)3, 0<x<1f_{Y|X}(y|x)=\frac{3y^2}{(1-y)^3},\ 0<x<1fY∣X(y∣x)=(1−y)33y2, 0<x<1BfY∣X(y∣x)=3y2(1−x)3, 0<y<1−xf_{Y|X}(y|x)=\frac{3y^2}{(1-x)^3},\ 0<y<1-xfY∣X(y∣x)=(1−x)33y2, 0<y<1−xCfY∣X(y∣x)=3x2(1−y)2, 0<x<1f_{Y|X}(y|x)=3x^2(1-y)^2,\ 0<x<1fY∣X(y∣x)=3x2(1−y)2, 0<x<1DfY∣X(y∣x)=3x2(1−y)3, 0<x<1−yf_{Y|X}(y|x)=\frac{3x^2}{(1-y)^3},\ 0<x<1-yfY∣X(y∣x)=(1−y)33x2, 0<x<1−y
