Hello,

Let X ~ U(0,1), Y ~U(0,1), and independent from each other. To calculate the density of U=Y/X, let V=X, then:

[tex]f_{U,V}(u,v)=f_{X,Y}(v,uv)|v|[/tex] by change of variables.

Then:

[tex]f_{U}(u)=\int_{0}^{1}{f_{X,Y}(v,uv)|v|dv}=\int_{0}^{1}{vdv}={1\over 2}, 0<u<\infty[/tex], which is not integrated to 1.

Where I am wrong?

gim

Let X ~ U(0,1), Y ~U(0,1), and independent from each other. To calculate the density of U=Y/X, let V=X, then:

[tex]f_{U,V}(u,v)=f_{X,Y}(v,uv)|v|[/tex] by change of variables.

Then:

[tex]f_{U}(u)=\int_{0}^{1}{f_{X,Y}(v,uv)|v|dv}=\int_{0}^{1}{vdv}={1\over 2}, 0<u<\infty[/tex], which is not integrated to 1.

Where I am wrong?

gim

Last edited: