If $X$ Unif~$[2, 5]$ and $Y$ Exp~$(4)$ are independent, what is the probability density function of $X + Y$ ?
I'm a bit confused about what the limits of integration should be to find the convolution:
We let $Z = X + Y$. Then,
$f_Z (z) = \int f_X (x) f_Y (z-x) \ dx$. I know the individual density functions, but I'm unsure of the limits of integration.