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Possible Duplicate:
How calculate the probability density function of $Z = X_1/X_2$

Need help with the following problem:

Suppose that X and Y are independent normal random variables with mean 0 and variance $\sigma^2$. Show that X/Y is a Cauchy random variable.

Hint: let U = X/Y and pick some V which is a function of X,Y in such a way that you can easily find X and Y if you know U,V. Then use the change of variables formula and marginalization.

I honestly have no idea how to solve this problem. All help would be appreciated.

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    This question has been asked and solved repeatedly on this forum. See for example, [this answer](http://math.stackexchange.com/a/77875/15941) by Sasha.2012-09-13
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    A general method is expanded on a specific example [here](http://math.stackexchange.com/a/30966/6179). // Any idea about the hint? There is a natural choice...2012-09-13
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    if you know that (X,Y) is invariant under rotations you can do it like this: $(X,Y) = R(sin(\theta), cos(\theta)), \theta $ uniform, $\dfrac XY = tan(\theta)$ which is the cumulant transform for a Cauchy.2012-09-13
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    @mike That is exactly the approach in [this answer](http://math.stackexchange.com/a/77906/15941) to the [question "How caclulate..."](http://math.stackexchange.com/a/77906/15941) referenced in my earlier comment.2012-09-13
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    sorry, i looked at one of the references.2012-09-13

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