Let $X$ and $Y$ be independent, each uniformly distributed on {1,2,...,n}. Find:
a) $P(X=Y)$; b)$P(X < Y)$; c)P(X>Y)
d) $P(\max(X,Y)=k) \text{ for } 1\le k \le n$
e) $P(\min(X,Y)=k) \text{ for } 1\le k \le n$
f) $P(X+Y=k)$ for $2\le k \le 2n$
I could do part a,b,c by using symmetry but not sure how to approach the rest of the problem