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Find the distribution functions of X+Y/X and X+Y/Z, given that X, Y, and Z have a common exponential distribution.

I think the main thing is that I wanted to confirm the distribution I got for X+Y. I'm doing the integral, and my calculus is a little rusty. I'm getting -e^-ax - ae^-as with parameters x from -infinity to infinity.

From there presumably I can just treat X+Y like one variable and then divide by z.

Thanks so much!

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    Tempted to suggest this related answer: http://math.stackexchange.com/questions/30938/given-pdf-of-i-and-r-both-i-and-r-are-independent-rvs-how-to-find-cdf-of-w/30966#309662011-04-18
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    Are you looking for distribution functions of $X+\frac Y X$ and $X+\frac Y Z$ *or* $\frac{X+Y}X$ and $\frac{X+Y}Z$. I'm assuming the latter, but you need parentheses.2011-04-18
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    Also, I guess you assume that $X, Y$ and $Z$ are independent.2011-04-18
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    It would be good to define the exponential distribution to indicate what $a$ and $x$ are. Also your result needs parentheses-presumably it is $-e^{-ax}-ae^{-as}$ (what is $s$? a typo for $x$?) but you have written $-e^{-a}x-ae^{-a}s$2011-04-19

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