Suppose $X,Y$ are uniformly distributed independent random variable on $\{1,...,N\}$ , compute the density of $X+Y$.
So the density of $X$ or $Y$ is $f_X (x) = \frac{1}{N}$ (so if we sum the terms, we get $1$). I believe that I have to use the convolution but not sure how to do this in the discrete case, I have:
$f_{X+Y} (z) = \sum_x f_X (x) f_Y(z-x) = \sum_x \frac{1}{N} f_Y(z-x)$, but now I don't know what to do. Any help is greatly appreciated, thank you.