I have the following density function
\begin{equation} f_{x,y\left(x,y\right)=\:\frac{1}{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:for\:\:0\le y\le x\le 1} \end{equation}
I need to find the probability density function for \begin{equation} Z = X+Y \end{equation}
Here is my works so far
\begin{equation}f_{X\left(x\right)=\:\int _0^x\frac{1}{x}dy\:=\:1\:}\\f_{Y\left(y\right)=\:\int _y^1\:\frac{1}{x}dx\:=\:-ln\left(y\right)\:}\\now\\_{Z\left(z\right)=\:\int _{-\infty }^{\infty }\:f_Y\left(y\right)f_X\left(z-y\right)dy\:=\:\int _{-\infty \:}^{\infty \:}\:\left[-ln\left(y\right)\right]dy\:} \end{equation} Which am stuck now on the limits of integration for the Z pdf. How do I find those please help. Thank you.