# Division of Two exponential Random variables

## Division of Two exponential Random variables

I have two exponential random variables $X$ and $Y$ with rate parameter $\lambda_1$ and $\lambda_2$. I have to find distribution function of $Z$ where $Z$ is given by:

$$Z=\frac{X}{Y+1}$$ and $f_{X}(x)=\lambda_1.\exp(-\lambda_1 x)$ and $f_{Y}(y)=\lambda_2.\exp(-\lambda_2 y)$. How to find pdf of $Z$ and How to check its validity?