Calculating the Density Function for X/Y with Exponential Distributions

[yinon]

X,Y r.v statistically independent ,with exponential Distribution.
calculate the density function of X/Y

(Let $X$ have distribution ${\lambda}e^{-{\lambda}x}$ and $Y$ have distribution ${\lambda}e^{-{\lambda}y}$

i know i should use transformtion u=X+Y ;v=X/Y to solve it)

 

[MarkFL]

Hello and welcome to MHB, yinon! :D

Can you show us what you have tried so our helpers know where you are stuck and how best to help?

 

[Fermat1]

Let $X$ have distribution ${\lambda}e^{-{\lambda}x}$ and $Y$ have distribution ${\theta}e^{-{\theta}y}$. Then $Y/X$ has distribution $\frac{\theta}{\lambda}e^{{\lambda}x-{\theta}y}$