Suppose that X and Y have the joint density given by fXYxy10

Suppose that X and Y have the joint density given by fX,Y(x,y)=10xy^2, 0<x<y<1.

Find the joint density of X/Y and Y .

Solution

a)

JointDensity of = f(x,y) / f_Y(y)

= 10xy^2 / integral (0->1) 10xy^2 dx

= 10xy^2 / (0->1) 5x^2y^2 dx

= 10xy^2 / ( 5y^2 )

= 2x Answer