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There are two i.i.d uniform random variables X and Y. Now I need to know the density of Y/X. My method is like this:

Let U=Y/X, V=X. Then the marginal density of U is what I need.

[tex]f_{U}(u)={\int_{-\infty}^{\infty}f_{U,V}(u,v)dv}={\int_{0}^{1}f_{X,Y}(u,uv)|v|dv}={\int_{0}^{1}vdv}=1/2[/tex]

Now the question is that my result 1/2 is not a reasonable density since it's not integrated to 1. Can anyone point out where I am wrong?

gim