# A Normal random variable divided by a Chi-squared random variable

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.

• How about this stats.stackexchange.com/questions/151854/… Dec 8 '18 at 17:10
• @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. Dec 8 '18 at 17:13
• @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. Dec 8 '18 at 17:14
• 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? Dec 8 '18 at 17:58
• This question has already been asked on this forum. I cannot trace it though. Dec 8 '18 at 18:38