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I am looking to find the pdf of the ratio $Z = \frac{X}{Y}$, where $X \sim$ Gaussian and $Y \sim$ Chi-squared are indepedent random variables.

A reference is good enough if you do not want to write down the complete solution.

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    $\begingroup$ How about this stats.stackexchange.com/questions/151854/… $\endgroup$ – user158565 Dec 8 '18 at 17:10
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    $\begingroup$ @user158565 that's normal divided by the square root of a scaled chi-square; which is not what this question asks. You might guess that OP has a mistake in their question (probably correctly) but it's best to make sure of it. $\endgroup$ – Glen_b -Reinstate Monica Dec 8 '18 at 17:13
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    $\begingroup$ @GAA your title question asks about dividing distributions, but you seem to actually be asking about dividing random variables; please clarify your title so it doesn't imply you're taking a ratio of distributions, but of random variables. $\endgroup$ – Glen_b -Reinstate Monica Dec 8 '18 at 17:14
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    $\begingroup$ Since GAA is new, I have edited the question to reflect what we think he is asking. GAA, can you please also clarify whether your Gaussian is standard Normal, or general Normal? $\endgroup$ – wolfies Dec 8 '18 at 17:58
  • $\begingroup$ This question has already been asked on this forum. I cannot trace it though. $\endgroup$ – Xi'an Dec 8 '18 at 18:38

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