I was asked to find the probability density function of $Z = X + Y$ (given $X$ and $Y$ independent). The pdfs of $X$ and $Y$ are uniform and given as $f_x(x) = 1/a, 0 ≤ x ≤ a$ and $f_y(y) = 1/b, 0 ≤ y ≤ b$.
My background in statistics is weak, and this came out of a course only tangentially related to statistics. So after refreshing and going through some stats textbooks, I learned a bit more about the subject, but still not quite up to the right level needed to solve this question.
I went to StackExchange, I found this, and it seems to have a plausible answer. But why are the bounds on the integration plus/minus infinity? Would I have to change that in my case as I have defined bounds?