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Where X and Y are continuous random variables defined on [0,1] with a continuous uniform distribution.

I know we define the density of Z, fz as the convolution of fx and fy but I have no idea why to evaluate the convolution integral, we consider the intervals [0,z] and [1,z-1].

I googled for articles regarding this particular example but so far every one I read seem to jump directly from integrating the convolution over the real number line to integrating it over these intervals. Why?

Thanks a lot for any help!