问题

The $n$ candidates for a job have been ranked $1,2,3,\ldots,n$. Let $X=$ the rank of a randomly selected candidate, so that $X$ has pmf
\[
p(x)=\begin{cases}
1/n, & x=1,2,3,\ldots,n\\
0, & \text{otherwise}
\end{cases}
\]
(This is called the discrete uniform distribution(离散均匀分布)).

Compute $E(X)$ and $V(X)$ using the shortcut formula. [Hint: The sum of the first $n$ positive integers is $n(n+1)/2$, whereas the sum of their squares is $n(n+1)(2n+1)/6$.]