Let $X_1$ and $X_2$ be independent integer valued random variables that both are uniformly distributed on {1, 2, . . . n}. What is the PMF for S := $X_1$ + $X_2$?
What I have so far: P(S=$X_1$+$X_2$) = $\sum_{i=1}^{S-1} P($$X_1$$=i, $$X_2$$=S-i)$ = $\sum_{i=1}^{S-1} (\frac1n*\frac1n)$ = $\frac{S-1}{n^2}$
But I don't think this is the answer because there is no way the probability keeps going higher as S goes higher. Can someone help me out please.