To Jan:

A reference you might find helpful:

http://www.dartmouth.edu/~chance/tea...k/Chapter7.pdf
Given your current knowledge, I think it’s instructive for you to think about how to calculate the pdf of $\displaystyle T = \frac{X}{Y}$.

The cdf of T is given by $\displaystyle F (t) = \Pr(T \leq t) = \Pr \left( \frac{X}{Y} \leq t \right) = \Pr(X \leq t Y)$ since Y > 0.

Therefore:

$\displaystyle F (t) = \int_{y = 0}^{\infty} \int_{x=0}^{x=ty} g(x,y) \, dx \, dy$

where $\displaystyle g(x, y)$ is the joint pdf of X and Y.

Since X and Y are independent random variables: $\displaystyle g(x,y) = \frac{1}{\lambda^2} e^{-x/ \lambda} \, e^{-y/ \lambda}$ for x > 0, y > 0, and is zero elsewhere.