- #1
gimmytang
- 20
- 0
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
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